Yes and no.
Most corps (and bands...including mine) have a UPS running for the express purpose of keeping the wifi network and mixer up and running, along with the sound engineer's iPad or computer. While you could theoretically run an entire sound system off of a UPS for a very limited time, it's not that simple. It really depends on the amperage draw of your amplifiers.
You would probably be ok in a pinch with a small system, but not with a system like most corps use, an certainly not on a regular basis. Would it work in a pinch in an emergency? Maybe.
Building a dedicated battery system is one option. I've seen bands that have several marine batteries with an inverter, but I've never used on personally. It would certainly be a lot more quiet than any generator, that's for sure. One of the band supply companies sells a pre-built rig along these lines, but I haven't seen any favorable reviews.