It could well be.

It's hard to tell if the fact Ishamael or Shai'tan did something to him so he could be an hound for the boys counts for anything in Fain's "power" beside his ability to sense the boys. Beside that, the amalgation of the two souls is probably responsible for what Jordan described as Fain/Mordeth having "unwittingly side-stepped the pattern after a fashion". It would make sense that the Wheel can't really control someone whose soul co-habits in a body with a second will/second soul which furthermore is that of a "ghost" that's supposed to be in the "soul pool". That comment is very important, as it seems to deny any possibility that Fain's role is predestined and part of what we can call the Wheel's plan, beyond of course the creation of SL itself, to serve in the Cleansing. But Fain/Mordeth appears to be an accident, and to have evolved into a real wildcard, one that can trump even a ta'veren.

I guess Fain's purpose may be to make a specific prophecy - one of those we're sure will come true in the endgame - derail at the last minute, producing a big plot twist and forcing the Wheel and Rand, and the Shadow alike, to find a new path. Something neither Moridin nor Rand is expecting and taking into account. No idea which prophecy it could be, though. If Jordan planned something like that, he would have made sure not to give us any clue.

Sanderson said Mordeth made much "unholy" research (that includes a visit to the Finns) in what could destroy the Shadow, and he found things. One of those things he found is driving him more than the others (obviously, it's the power/skills/philosophy - whatever it really is - that created Shadar Logoth), but apparently there was more than what we call "shadar logoth" in Mordeth's bag of tricks. And he still has all that, all that knowledge. Sanderson let slip somethign we suspected, that Mordeth's power came in part from the souls in Aridhol. It suggests the power of the Fain/Mordeth amalgamation may have risen through the series by either the souls of his followers (who kept dying) and victims, or - and I think it's the most likely explanation - from the fact he's capable of absorbing part of the power of Machin Shin by using the Ways so much. Machin Shin is fairly similar to SL, growing on souls of its victims.

Sanderson also said the power behind Mordeth is more akin to "soul" talents like wolfbrother/dreaming than to the OP and its talents. He described it as more instinctual/primitive than channelling the OP.

It really sounds like Mordeth has found various forms of primitive but potentially very potent "Dark Magic". Jordan no doubt has a complete explanation of how these "other powers" are related to the OP that's the driving force of everything in Creation, but I suspect that without his explanation we can't really describe it as more than "dark arts" (will we get clues to understand it better through Fain POV in AMOL? Maybe. Sanderson certainly seems to have gone deep in the Fain/Mordeth notes and it's most unlikely he did to be able to discuss Fain in Q&A). In part, in fact that'd be logical if the OP drives Creation as channellers believe, it seems to be alternative ways to draw the OP that have strictly nothing to do with the ability to channel it (it's confirmed by RJ neither Fain nor Mordeth have the potential to channel). Perphaps as some suspect, da'shain Aiel Singing/the Voice is yet another way to use the power in Creation without channelling it as those with the ability can (interestingly, Sanderson confirmed LTT was confused and delirious when he asked Ishamael if he had the Voice and about Singing happening in his house. He makes it sound as if LTT had lost track that it was the da'shain Aiel doing that). There's certainly the connection between Shadar Logoth and the da'shain in the fact they are absolute antithesis.

It's anyone's guess if what Mordeth/Fain does is strictly based in Creation (ie: ultimately, in the energy of the OP, just not in its pure energy form like channeling but drawing energy out of souls and so on) or if Mordeth also found ways to make use of Shai'tan's touch on the world to turn it against the Shadow, exactly like the taint of SL works against Creation. There was certainly no lack of creatures/souls touched by Shai'tan in his time... Shadowspawn were all over the world when Mordeth lived, made his research and applied some of his findings to create Shadar Logoth. I suspect personally it's both, I just don't think it's necessarily linked to the fact Ba'alzamon or the DO touched Fain, I think it may go all the way back to the Trolloc Wars and been part of Mordeth's powers all along.

Ultimately, it sounds as if Mordeth is transforming "power" from Creation into something as equally evil as the True Power and that can't co-exist with it. One way to see it may be that Mordeth's power is based on chaos, like the TP. Channellers can't break the order of "the system", they can't merge saidar and saidin for instance. They can use the OP for evil deeds of course, but they cannot make the OP itself evil, break it down to chaotic energy. But Mordeth can apparently transform the energy he draws somehow from Creation, or a mix of Creation and the invading TP energy, into chaotic energy. Quite a few things Fain did in the series were strikingly similar to what the DO can do (just nowhere as global or powerful, but still related).

I've never been that much of a fan of Fain to be honest (that owes a lot to the fact his storyline spanned the whole series and so advanced ever so slowly and Jordan never gave us much to understand where powers come from, we're stuck at "it's from SL and maybe the DO's touch" since TGH...), but his interest greatly increases with the finale. The Far Madding episode was the most interesting, and what we saw in TGS/TOM was quite promising.

Moridin obviously finds that Fain is an "important detail" to see to before the LB and that some things depended on Isam's success ats stopping Fain, but I think there's probably an interesting reason behind why he chose not to take care of him himself or send a Forsaken.

There was the big DH pack in WH too. Brandon RAFOed any question about what happened to them and who they were after. They're not connected to the ta'veren, or they would have killed Perrin that Moridin wanted dead. The rabid "taint" (the word is a bit too strong, it had not evolved into a real power like SL) of Masema was extremely similar to the Shadar Logoth taint, originating from very similar worldview of abandonning the ways of the Light in the name of the Light, which might well explain why the DH hesitated and circled the camp a few times before going. It's rather obvious they were after Fain. The question is more if we'll learn he dealt with them, or if they were a pack used by Isam to locate Fain that didn't find him, and we'll see another huge pack after Fain in AMOL.