I don't think so. Not completely anyway.

We know its a side effect of using the True Power for extended periods of times. The more TP you use, the more the Saa start to appear. But I don't think the exact mechanism of how the Saa appears is known. We also don't know how much you need to use TP before Saa starts appearing, though presumably its significant in that while the forsaken&Rand have all used TP, only Moridin has them.

Also, there are theories that the flaming eyes and mouth of Ishamael was a type of next-stage in the corruption caused by TP. A sort of super-Saa that you get when you use way too much TP. Being transmigrated to a new body seemed to reset the Saa counter implying that the effect is done to the body rather than the soul. Though Moridin has reached Saa-level even in his new body since he now uses TP exclusively and avoids saidin alltogether.

I think the amount of Saa in Moridins eyes has been slowly increasing as he uses the TP more and more. Maybe during the final confrontation (if there is going to be such a thing) with Rand, his eyes will be in flames again. That would bring him full circle.