It could make for an interesting theory. I will be honest, the thing that always stuck out to me about the Illithid is the fact that we have not seen what a natural born one looks like. The race as a whole are the creations from other races through a parasite, just like with the Xenomorph XX121. That makes a lot of question there for what they actually are.
Maybe in the future one of the two Gith races had developed a method to enrich the psionic potential of their race through an astral entity, or something of the far realm. That became the first Illithid.