It's implausible that Taim will become a Forsaken. Why? Because the DO has little use for the uneducated channelers of nowadays Randland. Also, the other Forsaken would only see it as an extreme slight (except monkey-boy Moridin, of course), and would kill his ass as quickly as possible. He would be "fresh fish" in their little prison of evil...
But maybe this will go in another direction... Since Taim "came out" before Rand did, he's probably just extremely jealous that it worked so well for our Al Thor. For Mazrim, a simple scholar from a lightly-populated portion of Saldaea (but who mysteriously eschews swords in the Borderlands), this is probably quite galling. It could very well be a case of simple jealousy, and once Rand unburdens himself to Taim - telling him how hard it was to reveal his true nature to his family and friends and the world - the two will realize that they have much more in common than they thought. Then they will start over again, but on common ground; Taim will see the Dragon's vulnerability, and realize that it mirrors his own.
And then slash fic fools everywhere will rejoice.