We kept a back-up copper line for about 5 years. In the end we decided that our cell phones were fine since 90% of calls go through them anyway. If cell service is unavailable, my UPS seems to work fine for the sorts of minimal power outages we get here. Don't see why a low draw wouldn't last about what calcs would show given the battery size you work with, the UPS only sees the draw and that is normally pretty linear effect on the battery.
The battery itself might be linear, but the UPS isn't - not at low power levels. The UPS itself uses power - I've seen numbers of about 10 watts for a 1000VA UPS. So if your load is 5W, then runtime calculations will be off by a factor of three (since the battery needs to supply 15W, not 5W). There may be other effects in either direction that I don't know about yet.
I just unplugged everything from my APC SUA1000, plugged in a 4W nightlight, and pulled the power plug. It stayed on, for 3 minutes at least. Yay.
However there are plenty of reports of other makes and models that DON'T work at low power levels, in addition to some reports that representatives of APC itself said, "their UPS won't function properly with such a low load."
There are lots of people claiming, with great confidence, exactly opposite opinions about this topic (
UPS for tiny load ,
How To Disable UPS Auto Turnoff? , etc.)
Unless you're the engineer that designed the thing, I think a few experiments on actual devices is worth any number of guesses.
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