MIRV,
Are you planning to use the SOLAR and your AC to DC CONVERTER at the same time? The CONVERTER has many more amps than your solar panel, and will most likely over-ride the solar and do all the charging. However, if you are in the wilds and not plugged in, then the CONVERTER does nothing, and your solar will do all the charging. There isn't anything to worry about having the solar connected all the time, it just offers no benefit if you are plugged in to shore power.
A 2000 watt INVERTER (if I understand you) is a lot of juice, you need a well designed 12-volt system to run such a beast. A 200 watt solar panel will cover the stand-by power on a big inverter as well the other parasitic loads on your system (DSI hot-water, DSI fridge, CO/LP detector, etc) ... maybe you will get some charging of the batteries during peak sun if all the variables align in your favor (by my educated guesstimating.) Look at adding more panels, or keep a generator handy :)
