Lead-acid batteries are far more tolerant than lithium batteries, though I hope they are deep-cycle ones ("Leisure batteries") rather than actual car batteries, if they are being used for general electrical equipment rather than vehicles? (Car batteries can only stand a few deep discharge cycles before being wrecked; deep cycle ones can't supply starter currents, but can be discharged and recharged many times).
The results you would get depend on both the generator and the charger types.
Generators usually have internal regulation to maintain the output voltage despite load and speed changes; that should hopefully minimise any voltage variation effects.
Chargers that use electronic voltage conversion (switched mode) are not too critical on input voltage, but too low a frequency may allow them to drop out and "restart" each half cycle, which could cause damage.
With an output of only 2.3KW, why use a generator?
I'd consider running a couple of high power rated vehicle alternators from the mechanical power unit. You can get after-market add on ones for running accessories or charging auxiliary batteries - just what you need.
120A types are readily available; two of those in tandem would allow more than the generator - and they are designed to work with a wide range of input speeds!
That gives you a direct battery-charging output, no separate charger needed.
You would need to work out an appropriate drive ratio so they were in their rated speed range despite drive speed variations, but if they were set up so normal speed was equivalent to say 2500 engine RPM (with the original vehicle drive ration) then the low speed would be equivalent to around 1000 RPM, and still give usable output, if somewhat less than the maximum.
(I don't know the exact drive ratio, on a normal engine installation? I'd guess the alternator runs at somewhere around 3x engine speed?? Other people on here can probably answer that).