At the risk of being a wet blanket (though not, for once, a canonista, since AFAIK there's no definite canon on the subject), I really can't see the Imperium spending much effort on spinning 4 and 5,000 year old history. No doubt there will be Imperiophile historians who will produce highly biased stinkers, but no more than the numbers of Imperioclastic hatchet jobs, and both sides will be despised by mainstream historians. And the Imperial Powers That Be will be sublimely indifferent. How much effort does the American government put inot spinning the collapse of the Roman Republic? How much effort do the Scandinavian countries put into covering up the murderous habits of the Vikings?
Nor do I think any of them will pay much attention to the history of pre-spaceflight countries, not even on Old Earth or Old Vland or Old Sylea. The history of the Terran Confederation and the Rule of Man is probably present (in a suitably vague and distorted version) in the Great Public Conciousness, but the fiddly details will be unknown to the great majority.
Why would the Imperium care about what people think of empires and republics in general? To Imperial citizens, the Imperium is unique. There's never been anything like it before[*]. Historical planetbound empires are different enough to be completely moot.
[*] OK, I'm getting a little bit canonista. sorry, I'll try to rein it in.
Hans