Thank you for the time scale. 5-15, plus decade is nothing in the timescales that they will be working with. So its definitly a possibility.If they torture the Engineers onboard the ship, and have access to the Computer Cores, I imagine they'd be able to create a Warp Drive cira Cochrane-era within 5-15 years, with comprable TNG capable Warp Drives within a decade there after. With the constraints you placed the Imperial Ships already, given that in this scenario, thier trying to recreate the native drive systems, they would eventually have to replace thier tech, with the Fed/Klingon/Romulan variety, until the Alpha Quadrant infrastructure could be updated to support Imperial tech.
In addition, you mentioned that you would have to give up Impeiral tech until some time as they are able to update local technology. They are hidden within the fringes of the galaxy, officially unknown to the Alpha powers. AT their main base, they have the means to reproduce Imperial tech. Not as good, of course, as it would be at home, but none the less Imperial level. This is taking a while, its not instantaneous, but they do have people who understand the underlining basis of Imperial technology. All this means is that they won't have to give up Imperial tech.
See, the goal is to understand the tech of the Federation (and other local powers) so as to be able to counteract any such things they do. Eventually, when the Empire declares war this will help them immensly. In fact, they will no so much about the enemeis but the enemies won't know anything about them.
In the same vein, I have another question that you all may help me with (its to small for its own page). I was wondering if you would thing that they need to change their name. I mean they are offically the Galactic Empire. Their leader was given the posistion of Grand Moff by the Emperor before his death. Still, they only control one small system. To introduce themselves as the "Galactic Empire" is kinda overdoing it. Thus, should they change the name to something like Pendragon's Empire (the Grand Moff is named Pendragon), the Empire, or keep it as the Galactic Empire and fudge the fact that they don't actually have a galaxy.
Thanks for all replies, it has been very helpful and interesting.