Would a UPS Fix This?

I have our Dish satellite receiver and 32" TV connected to a repurposed pure sine wave Tripp-Lite 600VA (375 watts) UPS. The UPS was given to me by a former employer when the internal battery died and they upgraded to a larger unit. Since the dead internal gel cell was 12-volt, I removed it, disabled the internal charger circuit and tied the battery connections directly to the coach batteries with suitable fusing. The Dish receiver and TV are perfectly happy with the setup , and the UPS is set to shut off if the battery voltage drops below 12 volts. I have not tested the setup for battery life, but I expect the relatively light load would run for quite some time. I do know it switches smoothly when an outage occurs and when the ATS kicks in after I start up the onboard generator. Battery life would be a question of load including anything else drawing on the batteries, initial battery SOC, and battery AH capacity, so answering that question would be difficult at best with any accuracy.