The answer is: "Maybe." And you can quote me on that. Jonathan Klawans lays out evidence on both sides of the question in "Was Jesus' Last Supper a Seder" in the Biblical Archaeology Review.
The Synoptic Gospels indicate that Jesus' final meal was on Passover:
On the first day of Unleavened Bread, when the Passover lamb is sacrificed, his disciples said to him, "Where do you want us to go and make the preparations for you to eat the Passover?" So he sent two of his disciples, saying to them, "Go into the city, and a man carrying a jar of water will meet you; follow him, and wherever he enters, say to the owner of the house, 'The Teacher asks, Where is my guest room where I may eat the Passover with my disciples?' He will show you a large room upstairs, furnished and ready. Make preparations for us there." So the disciples set out and went to the city, and found everything as he had told them; and they prepared the Passover meal. (Mark 14:12-16)
On the first day of Unleavened Bread the disciples came to Jesus, saying, "Where do you want us to make the preparations for you to eat the Passover?" He said, "Go into the city to a certain man, and say to him, 'The Teacher says, My time is near; I will keep the Passover at your house with my disciples.'" So the disciples did as Jesus had directed them, and they prepared the Passover meal. (Matthew 26:17-19)
Then came the day of Unleavened Bread, on which the Passover lamb had to be sacrificed. So Jesus sent Peter and John, saying, "Go and prepare the Passover meal for us that we may eat it." They asked him, "Where do you want us to make preparations for it?" "Listen," he said to them, "when you have entered the city, a man carrying a jar of water will meet you; follow him into the house he enters and say to the owner of the house, 'The teacher asks you, "Where is the guest room, where I may eat the Passover with my disciples?"' He will show you a large room upstairs, already furnished. Make preparations for us there." So they went and found everything as he had told them; and they prepared the Passover meal. (Luke 22:7-13)
However, the Gospel of John claims that Jesus was crucified at the time the Passover lambs were being slaughtered -- the day of Preparation (of the lambs, that is their slaughtering) -- making him a/the Paschal Lamb, meaning that Jesus died before Passover in John's Gospel.
Now it was the day of Preparation for the Passover; and it was about noon. He said to the Jews, "Here is your King!" They cried out, "Away with him! Away with him! Crucify him!" Pilate asked them, "Shall I crucify your King?" The chief priests answered, "We have no king but the emperor." Then he handed him over to them to be crucified. So they took Jesus. (John 19:14-16)
It is possible that John is theologizing, and I think very likely. What is interesting to me is the freedom that John feels to change the details -- or else the three synoptics have exercised such liberty. This is an important reminder, in a time when people are fixated on literal interpretations of Scripture, that the ancients were not interested in literalism -- not even when it came to the crucifixion.
Now, let's say for the sake of argument that the Synoptic Gospels are correct and that Jesus' last meal with his disciples was a Passover meal. Was it a seder? What is a seder?
The seder is a rabbinic refinement of the festival observance inaugurated in Exodus. The Bible records several phases of evolution for the observance of Passover. The first Passover in Exodus 12 is the pre-Exodus Passover. Exodus 13 provides the instructions for subsequent observances -- for example, they no longer have to eat with their sandals on, staffs in their hands, eating hurriedly as on the night of deliverance. The other books of the Torah continue discuss the Passover as one of the three pilgrimage festivals.
It may surprise you to know that there is no mention of the Israelites or Judeans observing Passover after the division of the monarchy. It may be that they did so and it was simply unnecessary to record or document the observance. But it may also be that they did not. Since the Bible was written and assembled beginning in the monarchy while the Temple was standing starting with older oral traditions and the Bible didn't exist as a complete collection until after the time of Jesus, individual people, people and some communities didn't have a Torah scroll on hand with all of the ritual instructions and explanations. When Jesus talks about the Scripture in Luke 24:44, he identifies it as, "the law of Moses, the prophets, and the psalms." That means that Job, Proverbs, Ruth, Esther, the Song of Songs, Ecclesiastes, Ezra, Nehemiah, Chronicles and Daniel (who was not considered a prophet in Jewish tradition) were not yet part of the Scriptural tradition at the time of Jesus or even at the time the Lukan Gospel was written.
When written scrolls were produced, different communities had different scrolls, no one community had all of the scrolls that would eventually be in the Bible, although many would have had the Torah. Perhaps, not even monarchs had those scrolls. And, arguably, one reason the Bible was produced was to establish, regulate and standardize religious practices. To illustrate the point, there is a story in 2 Kings 22 about the production and discovery of the first portion of a Torah scroll. I find it very significant that as soon as the Prophet Huldah verified the scroll as the word of God the next thing the community did in 2 Kings 23 was observe the Passover.
There is then another gap in the text: no mention of Passover until the exiles return from Babylon hundreds of years later. Indeed, many biblical scholars believe the written text of the Bible was produced in earnest during the Babylonian exile to reform Israelite religious practice and return them to the religious traditions of Exodus and the wilderness, including the observance of Passover.
The Bible doesn't describe the actual Passover meals in the accounts of 2 Kings 23 and Ezra 6:19-22. The biblical texts focus on the kosher slaughtering of the lambs, the timing of the pilgrimage and sacrifice and the joy of the celebration, not the family dinner table.
What happens at the table, the order -- that's the meaning of the rabbinic Hebrew word seder -- was not authoritatively standardized out until the rabbinic period. The rabbinic period is after the time of Jesus, inaugurated by the Roman destruction of the Temple in 70 C.E., leading to the development of a completely prayer-based Judaism instead of the combination of prayer and sacrifice that characterized Second Temple Judaism.
However, that the steps of the seder were codified after the time of Jesus doesn't mean that some of them weren't older practices. For example, many of the blessings that accompany Passover seders are also part of ordinary meals. And the three essential aspects of the seder as clarified by Rabbi Gamaliel (most likely the Elder): the sacrifice, the unleavened bread and the bitter herbs are all drawn from the biblical narrative and could have easily been in practice before the rabbinic codification.
It is possible that Jesus' last meal was a regular, but perhaps not ordinary, meal. The wine, bread and hymn would have been standard for meals. None of the Gospels specify that the bread Jesus used was unleavened. (There eventually arose a dispute in the church over whether to use leavened or unleavened bread in the Sacrament and practice varies widely.) There is no description of Jesus and his disciples eating lamb or bitter herbs, nor is it specified that their bread is unleavened.
One indication that Jewish first followers of Jesus regarded the meal as not being a Passover festival meal was the institution of the Lord's Supper as a weekly and even daily practice, like other meals. In addition, one of the earliest Christian witnesses, the Didache (or Apostle's Teaching), alluded to in Acts 2:42 the early form of the Eucharistic prayers closely resemble the traditional Jewish blessings said after meals, Birkat haMazon. The Didache is where Christians find the refrain in the Lord's Prayer, "for thine is the power and the glory," which is not present in many New Testament manuscripts.
And concerning the thanks-giving [Eucharist], give thanks thus: first, concerning the cup: "We thank you, our Father, for the holy vine of your son David, which you have made known to us through your son Jesus; to you be the glory forever. " And concerning the broken bread: "We thank you, our Father, for the life and knowledge which you have made known to us through your son Jesus; to you be the glory forever. As this broken bread was once scattered on the mountains, and gathered together became one, so may your congregation be gathered together from the ends of the earth into your kingdom; for yours is the glory and the power, through Jesus Christ, forever." But let no one eat or drink of your thanks-giving except those who have been baptized in the name of the Lord, for the Lord has said, "Do not give that which is holy to the dogs." (9:1-5)
Yet there is one aspect of Jesus' last meal that does not have a parallel in a regular or Sabbath meal, Jesus re-identification of the bread and wine with himself, his body and his blood. Jesus words would have also been stunning at a seder. They remain extraordinary.
Lastly, the association of Jesus last day and meal with Passover was made in earnest and deliberately by the early church.
Early Christians struggled over whether and how to observe Passover and over when to observe the Resurrection (should it always be on Sunday or on what ever day on the solar Julian -- then Gregorian -- calendar the 15th of Nisan on the Jewish lunar calendar fell?). The church struggled with this issue (the Quartodeciman controversy) for at least 500 years. The Gospels may represent this struggle with their differing portrayals of when Jesus and the disciples ate that meal.
So then, was Jesus' last supper a Passover seder? I don't know. Maybe. I actually think so. But either the evangelists didn't know or didn't care or the fact of the matter was subordinate to the ultimate truth they saw themselves communicating. The Gospels vote 3-to-1 in favor of the pre-rabbinic seder.