Oh, I definitely find that Varys theory plausible. I don't think he would sincerely be backing Cersei, but he does appear to be turning away from the Mad Queen.
If the Aegon thing had been set up on the show, I would think it likely that he's playing them against each other to clear the way for him. Maybe he's doing so for Jon.
Or, as mentioned earlier ITT, it could simply be Qyburn directing the little birds.