The quick answer is that voltage dip is generally not an issue when starting a VFD supplied motor.
I understand that there may be special conditions where voltage dip when starting a VFD supplied motor on a generator will exceed 10%.
We need the complete details of your application before we can give a good answer.
The specific question: "What are the potential impacts of frequency dip on a gen set?"
It depends on the reaction of the other loads on the set to under frequency.
The first impact will be the action of the "Under Frequency Roll Off" feature of the "Automatic Voltage Regulator".
UFRO will allow a 3 Hz drop in frequency and for greater frequency dips will reduce the voltage in proportion.
With a 13% frequency dip you can expect the UFRO to reduce the voltage setting by 10%.
A small UPS will often flash its light and beep. It will often pick up the load until the frequency dip recovers.
Bill
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"Why not the best?"
Jimmy Carter