There was one such fic in which chaos gods turn to Fulgrim as their champion.
In general the Heresy is much different as no other primarch has as much influence as he had, being the Warmaster and Emperor's favorite son. Lorgar and Fulgrim will continue plotting, Angron and Curze are sure to join, Perturabo is quite likely, but Magnus might stay loyal if there is no need to send an urgent message to the Emperor, which probably means that Mortarion probably flips due to his hatred of psykers and Magnus. I have no idea what Alpha legion will do with Horus staying within the light of the Emperor, but perhaps traitors can turn Lion?
No matter how many primarchs join this alternate treason, without Warmaster they will not command as nearly Navy, Army and Titan units as OTL and despite the power of the legions this is still a big deal.
There is good chance that Emperor doesn't end as corpse on the Golden Throne and Imperial Webway project is eventually completed.