Depends on how you define that. The UPS design will be the determining factor because if it is PWM and has a cap bank, there is an increase in current after a line interruption as the caps recharge. It will have a "pre-charge" current limiting circuit to keep it under control, but for a short time you will see a current surge of some limited amount. How long is not something you can know without talking to the UPS mfr. Then if the UPS has a bypass mode and it kicks in because the loads connected to the UPS demand more current that it can deliver, that will have to come from the generator directly.
