Not totally addicted perhaps, but it was described that Rand did have what might be called TP-cravings. He seemed to hold them off by using the Choedan Kal to get his "fix". If not for that, and given Rands insanity, it is not beyond possibility that Rand might have eventually slipped and used TP again.

I wonder for example if Rand was at all tempted to enter Far Madding and kill the in his mind traitorous borderlander-leaders with TP. What if he had not had CK or Nynaeve around, what would have happened?

Or the meeting with Tuon. Might he have convinced himself to draw just a little extra TP for safety reasons, if he had not had CK to give him that extra power.

And so on.