Just keep in mind you'll have to wire an on/off switch to the UPS, as it won't turn off automatically when power is cut to it. This means a constant, annoying beeping when power is off, plus it will drain its battery. UPS batteries aren't designed to be drained/recharged more than a few times, and the battery will probably die pretty quickly.
As long as you can extend the UPS's on/off switch to where you can easily reach it and switch it on/off every time you turn off/on your car, I don't see a problem with it. In fact, that would be a good way to make sure your carputer can survive cranks