I like this idea. It's a fresh take on an old trope, and could be very effective. I could see essentially two directions to go on this:
The Empire is Irrelevant: This largely sounds like the direction you're already going. The plot mainly takes place between the groups of protagonists. In this case, I don't think either the characters or the readers need to know the Empire is incompetent. If they find out, they should do it naturally --a raid is surprisingly successful, resistance is minimal, minions seem eager to change sides. However, in order to keep the audience from feeling cheated, you'll really need to keep the internal tensions high. Depending on whether you're going for adventure story or tragedy, the end of the book will either be that the heroes finally overcome their differences and subsequently find it comparatively easy to overcome the Empire, or that they defeat themselves, and the Empire endures without ever even noticing the rebels exist.
Satire: This could either be a broad or a bleak comedy. Incompetent comic antagonists are nothing new. If you're going for the funny, you'll essentially be writing Spaceballs. If it's a bleak comedy, then it's more or less the tragic version of the above"The Empire is Irrelevant," except this time, we see in excruciating detail, just how ineffective the Empire actually is, and how that still doesn't make any difference. --the political satire version of No Exit.