I don't see why not, especially if you had an eidetic memory like the Mike Ross character does.
There are a lot of common misconceptions about what goes on in professional schooling based, I imagine on some variant of the worst-case scenario our mind can imagine. For example, imagine having surgery performed on you by someone who never attended medical school. Terrifying, yes?
But surgeons don't become surgeons in medical school. They do so through internships and residencies after a lot of "book learnin'" and practice on things like cadavers. And while anyone who has had surgery should be pleased that once upon a time their surgeon first cut open a dead person, let's not mistake that for cutting open a live person, with blood flowing, a beating heart, etc.
Now, the law -- for all its complexity and arcana -- isn't medicine. There are huge consequences for making errors, but there are opportunities to read a statute twice, to proofread a brief for mistakes, to reconsider an argument. It's not like, "Oops I cut the aorta, the patient is going to bleed out here."
In law school, like medical school, the would-be lawyer learns a lot about the law, how to think about the law, etc. What he or she rarely learns, however, is the actual practice of law. You learn civil and criminal procedure, contracts, property rights, torts, legal methods and writing, et al. And the good news is, most law students then spend their time between years of law school being apprentice lawyers, either at firms or for judges or some similar work.
Mike Ross, a fictional character who never attended a day of law school as far as we know, has an eidetic (often called photographic) memory of a very advanced type. He can read large volumes of information and also process it. This makes him very well equipped, for example, to learn contract law, which is mostly about a lot of rules and their application in specific contexts. He similarly has the ability to read scores of existing briefs and other legal filings and rapidly understand what is in them. Since we are led to believe he is also intelligent, it shouldn't be stunning that he can apply his (1) knowledge of the rules and regulations against (2) existing successful templates of the work product he is supposed to produce.
Mike and his mentor Harvey both have another special ability, which is to come up with strategies to win cases or force settlements by exploiting weaknesses in their opposition or by seeing things in an unconventional manner. If anything, it is not entirely implausible -- once you accept Mike's intelligence and memory as givens -- that his lack of law school experience is helping him here. There is no class at Harvard called, "Winning Cases via Interesting Strategies" but you can bet that after 3 years together, a lot of Harvard J.D.s would approach similar sets of facts with similar ways of thinking. (Please note, I am not suggesting Harvard squelches independent thought or churns out legal robots, but rather than any institution that does things its own way is going to have a lot of people with a point of view.)
There are at least four states (California, New Mexico, Oregon, Minnesota as well as the District of Columbia) that don't require attending law school at all to take the Bar Exam* and become a lawyer. You obviously have to pass the exam, but you don't need law school to do that.
And for whatever it's worth, that's an interesting thought experiment to close this with: Do you think you know someone with a keen enough mind and memory that they could study for and pass the bar exam without having attended law school? Surely the prep work would be far more challenging and it might not be easy. But would it be impossible? Almost certainly not.
* Those states might well require you to do some combination of work other than attending law school in order to take the exam, however, For example, in California, this is acceptable: "Four years of study, with a minimum of 864 hours of preparation and study per year, at an unaccredited distance-learning or correspondence registered with the Committee."
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