IoM with Emprah is IoM when Emprah could do science, and not many persons more.In Fed any scientist is doing science.And Emprah must lost just like in canon - so IoM would get another problems to deal with.Fed must survive to that moment,not win.This is the Imperium during the Great Crusade. They are very much not the religious nutjobs of M42.
Also there's a point where no matter your cunning, your technology, your tactics, strategy and diplomacy, you will always lose to sheer numbers.
That's not winning though. All their main population and industrial centers would be with the Imperium and they'd be a few dozen ships at most, carrying what, a few thousand people? Eh.
And even if they lost and have dozen ships, after Heresy they would still have more scientific potential then entire IoM.few dozen ships after 10.000 years would become millions,including battleships capable of destroing entire IoM fleets.
So - IoM to win must destroy/capture all Fed ships, Fed to survive - even one ship with replicators and enough population could be enough to came back with venegance.