Charging the batteries with converter?

[TMfor4ofus]

We recently were fortunate enough to get a 2011 TM 2720. I'd like to know how effective is it use the converter to charge the batteries?? I'm assuming its all original and so how good is the converter at charging the batteries. Is it a smart or multi stage charger? It seems like after a night its charged up good. I found out it has 2 - 6v GC batteries. I was happy to see that and the date stamp says 7/15 so fairly new? We got a Westy 2400i Gen and I was wondering if I should go and buy a good 3 stage charger and power that off the Gen or is the converter sufficient? I only have 30w of solar which was okay for our 1 Gp 24 battery in our popup. If I keep them aimed at the sun and they actually get the batteries charged almost all the way on a good day if they werent discharged too much. The 30w solar is pretty useless on a cloudy winter day. I may upgrade the solar and so don't want to spend $$$ on a charger. ??
One more question is should I disconnect the batteries when sitting for even a couple weeks? Just pull the Neg terminal?