I know they tied their "Phase Cannons" into the Impulse Engines, and while they used EPS systems that shouldn't have been available until the early 24th century, when ever they lost Warp Drive, they still had most of their systems. As to an instance where they actually state that the ship runs on Impulse. It may have been when they were composing the letter to the school children in season one, but I can't be sure on that, its been five years since I've seen that episode. I don't even know if they ever come out and say it directly.
There's just no way the Warbird has only Impulse Drive, because it would take decades just to reach the Neutral Zone, if that were the case.
Just found my copy of the Official(the one seen on screen in BoT) Romulan Neutral Zone. The Zone is 12 light years in width. (as opposed to the 750 Parsecs that Franz Joesph's Peace Treaty established)