Over at Bolter and Chainsword there is a whole document looking at an alternate timeline! It's called the Dornian Heresy and looks at what if Dorn had been corrupted instead. It's good reading, especially the Index Astartes articles covering alternate loyalist legions.
Personally I think Erebus, Kor Phaeron, Lorgar and the Word Bearers would still have incited a heresy though it may have been less successful. By the time the Heresy begins the Night Lords have already gone rogue as their ranks are now full of murders and scum from Nostramo. The Iron Warriors had already committed genocide on their home planet's native populace so they would have little choice but to break with the Imperium, and it was only a matter of time before the Butcher's Nails turned the World Eaters into loons. Magnus was still going to dabble with sorcery which would still lead to a spanking from the Emperor and his wolves. As previously stated Lorgar was still going to be brooding over his rebuke from the big lad!
The Emperor's Children may or may not have escaped the predations of Slaanesh, but arguably given their personality they may well have trod this route without too much guidance from Horus.
If Horus didn't turn then obviously neither would his legion which was one of the largest at the time, and it is unlikely that without Horus's influence the Death Guard would have become traitors (though Old Canon suggests first captain Typhon was already corrupted.)
Without Horus turning then history and any sunsequent potential futures may have been altered so that the council of Xenos would not have challenged Alpharius and encouraged him to side with the Heresy in order to allow Chaos to consume itself.
Word Bearers - probably still traitor
Night Lords, World Eaters and Iron Warriors - renegades
Emperor's Children - Either Way
Thousand Sons - Still devastated , remnants go renegade
Sons of Horus - Imperial
Death Guard, Alpha Legion - Probably Imperial
Additionally Luther would still have been bitter about his banishment to Caliban so it remains likely that the Dark Angels would still have suffered a similar fate....
I think the Night Lords would at this point be unsalvageable as the majority were right little bastards having apparently been recruited from the cast of the classic British 1970's borstal movie 'Scum' (for those of you who haven't seen it, it is a film following a young Ray Winstone's experiences in a borstal/youth correctional facility in that decade...with a particularly heinous rape scene....horrible!) maybe the initial core of the Terran legion would survive, but these would be few in number.
I think the World Eaters would also be decimated, realistically only those original Terran Warhounds who had not had Nintendo's ill-fated 'Virtual Boy' (google it....it was a virtual reality headset console Nintendo released in the 1990's, apparently the games were good, but the chronic migraines it caused users were something of a problem) grafted to their heads would be permitted to survive as the rest of the legion are a ticking time bomb.
In retrospect Magnus might escape censure, as he will no longer need to send his psychic warning to the Emperor and thus will not break the giant Mecchano set that the big guy has been putting together beneath the palace. Thus the Emperor might be able to plonk old Magnus in the Golden Throne as he originally planned (either way things sound pretty shite for Magnus). Though the books imply the one-eyed ginger geezer had already entered some sort of pact with Tzeentch when he saved his legion from mutating into aardvarks at the beginning of the Great Crusade.
I still think the Alpha Legion would have escaped corruption as the Eldar and chums would not have needed to approach them in 'Legion'.
Luther is likely to still sulk, but with the heresy not happening he might just grin and bear it, or the Lion could come back and give him a proper spanking!
Hmmmmm what would the Emperor have done post crusade? Good question. I don't think he would have ascended to Godhood, he would have probably have continued to rule but with the Council of Terra as his right hand, not the Primarchs.
With the galaxy conquered the Astartes would be pretty useless, and maybe a bit of a problem (similar to British Soldiers returning home following the conclusion of the Napoleonic Wars and generally being a nuisance). Perhaps the Emperor may have done the unthinkable and wiped out the Astartes, culling them all....no you cry, yeah, well I bet the Thunder Warriors were quite surprised when the Custodes turned on them at the end of the Unification Wars...thus we have precedent here!
Then humanity could rely on the might of the massive Imperial Army to defend them when needed, and if a new enemy cropped up that needed a stronger measure the Emperor could use his Custodes as a stop gap while he popped into his bunker, cracked open his 'Chemistry for Immortals' box set and brewed up some new Space Marines.
Well what do you think?
PS can someone go look at my battle report in the sixth edition forum (I know I normally play Rogue Trader and 2nd Ed, but I feel I'm growing as a person) it took me ages to write and I included pictures....I need to feel some love!)