Depends on the type of UPS:
- Offline UPS - normally power runs through it directly to its load. When external power drops, a relay switches to running the inverter off the battery. Slowest react time.
- Line interactive - actively manages input to provide a cleaner output to the load. Inverter is always in the loop, rather than being activated at need. This lets it switch power much faster, often within a handful of milliseconds.
- Online - power always runs “through” the battery. External AC power is converted to DC and fed to the battery. The battery outputs DC to an inverter which converts it to AC for the load. There is no switching time because the power path never changes. Best type, but wears out batteries regularly; schedule replacements every year or two.
Another thing to look for is true sine wave output. Most affordable UPSes provide either square wave (ugh) or step-sine (also ugh but less so). If your protected hardware has AC motors, those waveforms will risk damaging them. Probably not a problem for a 3d printer and it’s DC servo motors.
All seems a bit silly to me. I’ve had power fail during a print. My P1S started right back up, resumed the print and finished flawlessly. But I suppose a UPS is at least good protection for the machine, so if it makes you feel better to have an orderly shutdown, why not? 
(I’m that idiot with a rack mount online UPS running my home network, servers and WiFi. Power may go out but our internet does not!)