The power at 400hz, when the voltage fluxuates, the reactive drops through the system are even more significant, up to 7 times the difference. Typical chargers are not set up to handle this voltage swing, especially the drops.
The batteries are then subject to this flux, and it degrades them in respect to 60hz charging.
A 400Hz 115 volt alternator is extremely stable, as they are mounted to systems that keep their rotation speed constant (it called a constant speed drive for that reason) If the voltage fluctuated, then there are a lot of electronic systems that would be damaged. ( alternator is controlled by a voltage regulator to keep it stable). Yes, output power can vary, that is due to changing requirements of the load.. IE the current supplied varies due to changing demand.
If the plug pack works at 400 Hz (I have never tried to do it) then its output will be the required 5/9/12/20 volts that it is designed to provide. If the power pack has a transformer in it, then its impedance will be very high at 400 Hz (about 6.5 to 8 times higher depending on its design frequency) then its ability supply current will be reduced.