For many, the immediate response would be a resounding "no!" Within the theistic traditions of India and within the theistic traditions of the world, there are varying opinions on the subject. For some, it's not too difficult to understand the energy and presence of God in nature and even in one's self. There are numerous verses in the seventh and ninth chapters of the Bhagavad Gita supporting this point.
I am the taste in water, the light of the sun and moon... I am the original fragrance of the earth, and I am the heat in fire. I am the life of all that lives... Everything rests on Me as pearls are strung on a thread. Of the senses, I am the mind and in the living beings, I am consciousness.
The school of thought accepted by the majority of practitioners within Hinduism is that God or the Supreme is an all-pervading and all-powerful energy without form or qualities. I suppose this is a natural conclusion for many to arrive at. There is no doubt it is extremely difficult for one to conclude that the essence of everything as described in the above verses, who is creator of all that we see and experience in the world and universe is an embodied being. A person pursuing liberation with this notion of God, is supposed to, upon death, leave this material body behind and become one with the Supreme by merging into the all-pervading impersonal energy.
However, according to the Bhagavad Gita, the soul is eternal, active by nature, and can never be destroyed. The soul can merge into the Supreme, but can't remain in that inactive state perpetually. The soul needs activity and interaction with others and it's especially hankering for a relationship with God.
In human experience, we've never come across a perfect being. Rather, we see people having certain fallibilities such as imperfect senses, the propensity to cheat and exploit others, and the tendency to commit mistakes. We then automatically project those same assumptions on to God and therefore come to the conclusion that God can't have a form or personality.
When I had first started studying Gaudiya Vaisnavism, the monotheistic strand of Hinduism, I came across a different school of thought, which was initially very confusing and difficult to understand. It proposed that God, in addition to possessing impersonal features, had a personality with names, forms, qualities and activities. After grappling with this idea for a few years, I finally started to become comfortable with it and gradually even began to appreciate it.
The Brahma Samhita, a prominent scripture within the Gaudiya Vaisnava theology, explains the nature of God's form and qualities.
I worship Govinda (Krishna), the primeval Lord, whose transcendental form is full of bliss and truth, and is thus full of the most dazzling splendor. Each of the limbs of that transcendental figure possesses in Himself, the full-fledged functions of all the organs, and eternally sees, maintains and manifests the infinite universes, both spiritual and mundane... He is without a beginning, whose form is endless...yet He is a person possessing the beauty of blooming youth.
In the fourth chapter of the Bhagavad Gita, Krishna explains that He reciprocates with individuals according to the way they approach Him. The goal of life described by many spiritual traditions is to develop a loving relationship with God. Love has to be reciprocal which means, love can only exist between two or more individual sentient beings. We can't love something inanimate simply because an object can't love us back. We like to make the claim "I love my car or I love my hair..." but that's not love because your car or hair doesn't love you and it really can't love you in reality.
Even though it may sound attractive or may be easier to understand that God is formless energy, as far as I'm concerned, it's not possible to exchange love with formless energy. We might offer the argument that imposing a personality upon the supreme is limiting Him, but who are we to say He can't have a form.
It's natural for us to try and use our mind and intellect to comprehend God's form and energy, but very quickly we come to realize that we just don't have that capacity, just as we don't have the capacity to understand the universe and how the whole thing works. Just as we can't fully understand another person without them letting us into their lives, we also can't understand the personality of God by force or the power of our intellect. Krishna explains in the Gita that He reveals Himself to those who desire to have a loving relationship with Him and ultimately, we're all looking for loving relationships with each other and with God.