A UPS will keep everything connected to it powered up during a power interruption, up to the length of time the battery can support that load. I used to have a UPS connected to our home TV, satellite receiver, and sound system as power interruptions were not uncommon. It died a couple years ago and I have not replaced it even though our semi rural area still has the power issues.
An inverter is s good idea if you can reasonably isolate that circuit or pull a new one. And knowing it will be pulling from your coach battery and possibly draining it if left too long.