You have to believe this is not a 5th wheel asyou already stated the instability issue without the generator. Adding any measureable weight to the tail of this unit, especially if a bumper pull, will have a noticiable effect.
If noticed, when buying a unit with a built in generator, they are generally right up front due to their weight and necessity to keep the weight distribution properly on the hitch.
"Old Farmer" is right, go to the scales and check on the tongue weight before going too far. Worst case scenario will be to load the generator inside and take a couple of strong kids with you to move it.
Bob and Better Half
2007 F-250 PSD, SW, CC, LB, 2WD
2006 TF32SS Cross Terrain Toy Hauler (sold)
Reese 16k slider