Depending on where you are located and how you camp, it may be worth looking at solar as an option. I am in the southwest, installed solar, and never use my generator any longer (except for AC, which I never use when boondocking). It is not super cheap but is quiet and just works.
To your question; assuming you are connecting that generator to your shore power connector and you do not have a large load running in the MH, yes, it would charge the batteries.
It kind of sounds like an energy audit/budget is in order. My long description is here
but the short version is to add up the power consumption (in watts) of all the items in the MH that you use and the length of time you use them. From this, you can see how much power you require every day and then make good decisions about how to supply that power.