Next question, are consumer-grade UPS units like that capable of being run continuously?
I believe the answer to that is no. At least not if you want to run them at a substantial fraction of their maximum rating. Consumer UPS are only designed to run from their internal battery, relying on the fact that the battery will run out before the rest of the UPS needs to worry about overheating from heat buildup due to passive cooling and minimal case venting. With only 3-5 minutes of battery backup time under full load, the transformer(s) and heatsinks are still warming up by the time the battery cuts off. If you run it at 1/4 load, that causes 1/16th the I2R losses and the UPS might be able to run that indefinitely if you hacked external batteries into it.
When you get into higher capacity units that support external battery packs, like APC's BR1500G, you get a fan to keep things cool over the massively extended run time. Those should be able to run continuously since they are already designed to run at near 100% load long enough to reach steady operating temperature.