I think this is an area of semantics and opinion, which the generator and/or UPS manufacturer will spin in their favor. Possibly no two generator models behave the same and I can offer only one example, an Onan "microquiet" RV generator with AVR. This is the no-load voltage output:
The AVR distorts the output with a reactive load, in this case an air conditioner. This situation isn't in play with a UPS:
Switching regulators, which I assume go hand-in-hand with most UPSs, are non-linear loads which the AVR really doesn't like. This shot has a switching battery charger as the load. By comparison, a Honda inverter generator in the same situation does a whole lot better (AVR on left, Honda inverter on right). Voltage on top trace, current on the bottom:
<<<AVR -------- Inverter gen>>> 
When adding a purely resistive load in addition to the battery charger, the AVR behaves better:
From this one example, I'm not very impressed with how AVR generators handle high PF loads, which a UPS likely is.