it's more like how much inverter do you need, but i'm quite sure you can charge your batteries with the generator you listed. a 2000 or 2500 can charge up even with only a 15amp shared shore power, so the generator should be fine. i've set my 2000w inverter/charger to use 15a shore power so that i can keep computers, refrig, and tv on without blowing a breaker.
does that help?