EMS units are recommended for use with commercial power only

Actually there is no need to use an EMS with a generator
Most will not continue to run with a load so heavy that it drags the output voltage too low
And a generator is not going to produce the transient spikes and sustained high voltage surges that can happen on utility power

They make it quite plain, use it with commercial power ( they just don't want to try and detail everything else that might be ok )
Should it work with a good generator?
Yes..It should
But it's not needed !