Most UPSes are not designed to work from a generator, regardless of load. Generators vary the frequency and sinewave shape as they attempt to regulate the output. Or put another way, generators are not good at holding the frequency and sinewave shape as loads change.
Most UPSes monitor multiple items, each of which can be a basis for switching over to battery power.
- Line Frequency
- sine wave shape
- Line Voltage (RMS)
- Line Voltage (Peak)
There might be others, but these are the ones I'm aware of. You can test your setup by simply running your generator with the UPS plugged into it (no other loads). See if the UPS behaves. I'm betting that it won't. Most UPSes will simply oscillate back and forth until their batteries are dead.
To solve this, one needs to have what is called an inverter output from the generator.
Honda makes some
Unfortunately I have not seen any systems where you can add an inverter to an existing generator.