If it's a multi stage charger you should be alright. It'll go into float when the batteries are charged. Some new chargers like my MH will actually stop charging all together if needed and turn back on when charging is required. Google your model and see what it says.
We've had Flow Rite battery watering system in our last MH and I installed it in this one too. Yes you fill the batteries by squeezing distilled water from a jug into them. Doesn't use hardly any water at all. Monthly is more than enough. Unless you cycle the batteries often by using the invertor.
But do monitor each individual battery with a volt meter every month to make sure each battery is ok.