Okay, the big question is "when the gods leave, does it include the godlike beings such as archefey and demon princes?"
Because if Asmodeus goes but not Orcus or Demogorgon, the demons have a significant advantage, and very well might "win". Especially as they retain their leadership while all of Hell is battling over succession.
If all gods and god-likes leave then that's a different story. While the demons have lost all their leadership and control, the devils still mostly have their hierarchy and a bunch of pit fiends assume control of the Nine Hells. The Blood War can continue or the devils could direct the demonic hordes towards the fey and angels.
But I think another party might have a chance.
Mortals lost divine magic and, in many worlds, arcane magic has lost its divine control and might run wild. Demons are overrunning the Outer Planes wildly until all the other planar beings step up to eliminate them and scourge the Abyss at great cost.
Meanwhile hidden beneath the mortal lands, the most intelligent and cunning being left in the multiverse coordinate and scheme. They wait until all is settling and their enemies are at their weakest. Then the Elder Brains and their illithid children arise to take over the world...