In the "First Heretic", Lorgar meets a demon guide Ingethel, which shows primarch the "truth" about Chaos. Ingethel also says, that "Chaos will be humanity's salvation, godless empire will fall to the claws of aliens, when humans will follow the fall of Eldar".
Was the demon lying?
The Eldar fell because their Cult of Pleasure created something horrible, something that they weren't able to accept as their god, hence Slaneesh absorbed them (body and soul) into himself. The Imperial Truth was atheistic dogma, so would it mean, that Empire would create a Chaos god of... atheism? It doesn't seem too plausible, since the Imperial Cult was already taking hold and, in the long run, it wouldn't matter would Emperor be worshipped as a god or just a immortal hero.
Or maybe there is another explanation - victorious Empire without Horus Heresy would easily conquer whole galaxy and wipe all resistance. Following that, without any threat it would start neglecting the military, leaving it open to the arrival of Tyranids some ten thousands years later?