This issue may have come about from years gone by.
Nearly all sets were limited by engine power. The simple solution was to supply a bigger generator so engine would sulk at over-load rather than burning the generator windings , while a big engine on a smaller generator would just bark and keep driving the genny until the winding insulation melted - expensive failure.
These days with the modern circuit breakers (fuses at overload would not necessarily melt before the windings overheated), that is a scenario easily avoided.
However you may well trip the circuit breakers at the least overload and wouldn't hope to start large electric motor loads. So you are stuck between a rock and a hard place!
You will utilise that energy in the flywheels only as they slow down. If they slow down too much, frequency will suffer likewise, volts will suffer, depending on excitation, so it can only be a transient overload or the motor will not start. Yes there is plenty of momentum in the flywheels, but that was primarily designed in for speed stability, not for overload conditions.
I would think it would depend a lot on starting load on the motor and type of motor. I would never want to go near the point where starting might be a problem as something will get burned at some time unless all the modern trip safegaurds are employed.
A better way might be a transient increase in engine speed just before the load contacted. I have had to do this, in the past, to get a freezer to start with a very small generator. !0% should be more than enough or you would be needing a bigger set altogether.
A better way is to actually look at the odd item that you may have difficulty starting and substitute a better alternative for that. Modern well pumps are much(?) more efficient than ancient ones, I presume.
Always better to cure the disease rather than the symptoms, in my view.
Regards, RAB