I've seen it happen. When on the genset, the load burdens then slows the generator, which lowers the frequency as the voltage drops. So that actually is what a VFD does too, meaning you will actually get MORE torque per unit of current than if the frequency was correct. Then the generator brings the motor up to speed with it as it recovers from the step change in load. The first time I had this happen was at the Ford Island Bridge in Pearl Harbor, the drawbridge you go on to get to the USS Arizona memorial. When running on the backup generator, the starters worked to power up the hydraulic power units but when connected to the utility power, they tripped on OL before they could accelerate the motors. I got a free trip to Hawaii on that one. I tweaked the settings on the Soft Starters in about 10 minutes, but didn't tell anyone for 3 days...
The tricky part is that the Soft Starter must be tolerant of the frequency drop and continue functioning. Some are, most are not. So MOST of the time, the soft starter will trip on Under Frequency and nobody knows that it MIGHT have worked if it had not tripped first. But Nordic Soft Starters (and A-B and Motortronics who I worked for) use a somewhat unique firing circuit, so they are (were) insensitive to frequency drift. Nordic was part of Furnas who was bought by Siemens and is now gone, the only remaining product that Siemens sells that is made from that older technology is the 72G, because getting approvals on elevator controls is a logistical nightmare and incredibly expensive. So Siemens wisely left that product alone, selling it exclusively to elevator OEMs.