In addition to charging the battery, the converter usually performs your breaker/fuse panel function and runs the 12v systems independently of the battery when shore power is present, so its probably best to keep it.
The inverters with battery chargers you're probably thinking of (and certainly those that might have the house breaker/fuse panel function built in) are I believe more suited to class A motor homes with lots of battery power available and lots of AC devices to run without shore power present.
When boondocking, even with solar power back-up, your capacity to run high power AC devices such as a microwave is virtually nil, so you probably want to stick to a small inverter without a battery charger so you can just run some low power AC devices (e.g. TV, laptop, etc.)
Just to confuse you even more, a solar kit usually comes with a charge controller (Arghh, how many battery chargers do I need?!!). This merely conditions the "raw" power from the solar panel so it is suitable for battery charging.
-Paul
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