I think during the 13th Black Crusada chaos HAD a huge foothold, but they've been driven off since. I don't think the Imperium would allow any Chaos power to establish itself on Cadia as long as a single soldier within the Imperium draws breath. Not to mention that a foothold would likely draw Chaos like nothing else.
Lexicanum however says that you're right, they have a major foothold, but no reinforcements from space, and since, at least out of game, the 13th BC is a few years past already, they might have been driven off since.
Chaos "won" the campaign, though, because,a s far as I remember, they captured a lot of the surrounding planets.