UPS might carry you past the voltage drop, or it might not. My experience over the years has varied. UPS has carried most of my PCs through short-term power failures, but there is a finite switching time, and some electronic devices have absolutely no reserve or inertia in their power supplies to carry over the switching time.
For example, of the items I currently have on UPS, my desktop computer, router, external network=attached drive, and cable modem survive the switchover, while the cable TV box and Samsung TV will reboot. I had a Sun SparcStation on UPS that would reboot when its UPS switched over to cover brownouts, yet it would keep going fine through the brownout itself, so we took that one off UPS.
You should expect a UPS to cover you, but no guarantees.
You might be better off running that TV off inverter, which is like having it permanently on UPS with no switchover.