One problem is that the semi canon dark urge is a dragonborn.
If we ignore the (infertile) transformed humans for a moment dragonborn only appeared during the spellplague at which point Bhaal was already dead. So whatever connection the Urge has to Bhaal had to be created after Bhaals rebirth which was 10 years before the game.
Its more likely that the dark urge is Bhaal with amnesia.
If this is Bhaal with amensia, he should have a divine rank and a very high power at the start of the game, which obviously will not happen = This is not Bhaal
