They are listed in the MM as Mind Flayer Medium aberration , lawful evil and Intellect Devourer Tiny aberration , lawful evil and there enough lore to make me believe that they are could be from the Far Realm so I have no trouble believing they could be related to a Great Old One.
OK, I see your point. I don't think, that Ilithids and Cthulhu have that much in common apart from the look. Mindflayers could be a servant race to Cthulhu or another Great Old One from Lovevrafts stories.
"We are all stories in the end. Just make it a good one."
