Both Shar and Tiamat (and other evil gods) have posed as good gods for one plot or another. Sometimes just to gain more followers that wouldn't normally worship them. So I could see that.. kind of. Seems to simple as a plot point.
The Illithids had nautiloids in spelljammer, so even if they can't make them anymore, doesn't mean there aren't still a few (or a lot) still out there. And remember, it was one of their enemies that said they lost the ability to make them, might not even be true.
MINOR SPOILERS FOR THE RECENT RA SALVATORE BOOKS - There was something about Lolth and the Illithids that I would say more about.
IMO, it's deffinately NOT a Bhaalspawn, but it wouldn't be a Baulder's Gate game with someone trying to become a god.
The Githyanki capital city is built on the corpse of a dead god the floats through the astral plane, and Tiamat is already (at least a little) involved through them.
Are there actual clerics of the Absolute, or just cultists?
There are UR priests in older D&D editions, who tap into the raw divine energy to cast and are in fact atheists.
Could be an Elder brain that found a way to pause the ceremorphosis. Uses it to create a cult. Cults mean worship. Enough worship and the Illithids get their own god....which would be superbad for all the Realms and the other gods too, as the Illitids are from Outside.
