Probably not the ideal solution but it could work. I seem to remember one UPS that refused to power-up if it did not initially have a live AC input. I think that was because it was a rather small UPS intended to keep the comptuter alive only long enough to quickly save WIP and "safely" shut down. You wouldn't want to turn on a computer that was already off because it would only last long enough to boot. Long story short, you might want to test yours.

I have an old UPS with worn out gelcells I'm thinking of replacing with some large deep-cycle batteries. It could be used to power my furnace during short power outages.