I don't think the Dark One would allow Rand access to the TP. He doesn't know Rand, certainly can't trust him to do his bidding, and Rand is probably the most uncontrollable individual out there (we know the DO's a control freak). We know that Rand and Moridin's threads are connected somehow, and we know that there's a connection when they channel as well: Moridin becomes nauseous when Rand grasps the OP.

With this in mind, I think we have a good enough setup to exclude Rand channeling the True Power directly (the DO wouldn't have allowed it), and to include Rand channeling through Moridin via his link.