Dungeons and Dragons

I think that's possible and can certainly be your head canon or what you run at your table.

That said, I believe the connections between the two are entirely due to the githyanki's enslavement by the illithids. Learning the wrong lessons from their oppressors is a sad, but not unbelievable, outcome. The note about aboleths is interesting but I'm not familiar enough with their lore to effectively speculate why they would not know about illithids - perhaps they just didn't come into contact with them until the height of the illithid empire.

This kind of lore stuff is why I stick to homebrew tbh

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.