What kind of TV? (CRT, LCD, ???)
How big?
Check the label on the back, what's the listed current draw?
My concern off the top of my head: If it's a CRT, it'll have a degaussing coil, which is likely to receive a pulse of electricity at power-on. Higher quality units will have more powerful coils. If you would turn on the TV while it's running on backup power, that will likely be too much for the UPS.
I had a lovely 21" Nokia monitor (Trinitron tube), and its degausser was very powerful; my 1250VA UPS complained about a brief overload (just when running off of line power) whenever I happened to use the degauss function.