As long as you're using the same or larger capacity rechargeable battery of the same voltage, you should be OK.

A car battery should work fine for a short-term solution, but I wouldn't recommend it for continuous indoor use. Remember, too, some batteries have differing charge/float voltages.

The chargers in the small UPSs are usually puny. A large battery will take a long time to charge. An external AC charger is recommended. I picked up a Black & Decker car charger that actually has settings for AGM, GEL and wet cells.

Some of the high-end small UPSs "sense" the slower voltage rise and will generate a bad battery alarm. It won't debilitate the unit, but it might beep or send you a notification (for units connected by USB/serial).

-josh