Generator Undervoltage Condition

yes

If one can fully trust the AVR then one doesn't need a U/V Relay at all. U/V Relays are needed to detect and act during abnormalities such as failure of AVR to maintain the terminal voltage.

However, the situation is not so alarming that it calls for a trip and shut down of the generator. Only an alarm will do.

However with today's numerical relays, you can set two levels of settings for the U/V condition, one for an alarm, say at about 80% and another level for trip, say at about 70% of the rated voltage.