I've seen some APC UPSs that will appear dead if they don't have a battery installed. But if you connect a simple little wall wart, it starts up fine. It just needs a tiny amount of battery voltage to allow it to wake up.
Once it starts up, you can talk to it, configure it, whatever. It might be able to provide voltage boost and cut functions if those don't need a battery. Some UPSs use the battery for voltage boost, some don't.
Larger batteries are fine, up to a point. If you install a huge battery, you might burn out the battery charger circuitry since it would be pumping out maximum current for days trying to charge the behemoth.