The short answer is “Probably not.”
All Generac permanent residential air-cooled generators are floating neutral generators. The neutral conductor is not bonded to the equipment grounding conductor or to the generator frame.
All Generac residential automatic transfer switches have either a 2 pole (single phase) or 3 pole (three phase) switching mechanism and have a solid neutral connection. The neutral conductor is not switched upon transfer from the utility to the generator source. The generator neutral conductor has a direct electrical connection to the utility neutral conductor and the grounding electrode system at the service.
This is the definition of a “nonseparately derived system” and is also why NEC Article 702.7 (B) requires a warning label on the service equipment that states "a shock hazard exists if grounding electrode conductor or bonding jumper connection in this equipment is removed while the alternate source (generator) is energized.”
All that he NEC requires in 250.35 for grounding a nonseparately derived system generator is that a conductor that provides a fault return path be installed with the generator feeder conductors. The equipment grounding conductor that is part of the four or five wire feeder from the generator to the transfer equipment will ground and bond all of the non-current carrying metal parts of the generator through the transfer equipment to the grounding electrode system back at the service.