I have actually looked into a battery back up quite seriously. NO a UPS will absolutely not work at all. Most are designed to run 300 watts for a max of 20 min. You might get 30 or 40 tops but that likely isn't long enough.
The controller for the incubator matters a lot as well if you are running a pulse proportional (herpstat/ Helix) the inverter (or generator) MUST be a pure sein wave inverter. Most on the market are modified sein wave and Dion at Spyder robotics told me that this can cause the unit to 'stick' wide open 100% power with out shutting off. To the best of my knowledge only Honda makes pure sein wave inverters.
It is possible to design a battery back up using deep cycle marine batteries running a pure sein wave inverter that can be triggered to switch on after a power failure (that takes about 30 seconds) A small incubator depending on how cold the space it is in gets and how efficient the unit is it could be used for 12-24 hours. I have been talking to a electrical engineer to design a similar unit only not for an incubator but to run a back up heat source for my collection to keep the enclosures at 82-85º for 24 hours off a battery it is likely going to be fairly expensive... Just electrical components no heat source and just a simple 1 degree throw thermostat and it looks to be well over 500$ the inverter is 475$ alone.
A automatic generator is likely not a bad option. Check the specks on the inverter that it uses the cheap ones likely will cause controllers to fail.