Yeah, I too used this trick many years ago when doing remote broadcasts for the radio station where I worked at the time. Mounted an ancient industrial-grade TrippLite in the van, wired it to the aux battery stack, and used it to power the few pieces of gear we had that wouldn't run on 12 volts.
A potential caveat- many (if not most) modern consumer-grade UPSes will not self-start. In other words, you can connect a healthy battery to them, press the front panel button, and absolutely nothing will happen unless they're plugged into the wall. For whatever reason, it seems that many of the units I've come across will only turn on the inverter if they are first connected to an active mains connection, turned on, and then the mains plug pulled from the wall.
Older units (by which I mean at least 10-15 years old, at this point) don't seem to have this problem. It might also just be something unique to consumer-grade stuff, I've not exhaustively researched the issue.