Electrically, the fireplaces are usually just space heaters. If you can run a typical electric space heater, you could run the fireplace.
Assuming you want it on its own breaker, you'd have to see if there is space for a breaker or the option of swapping a single breaker for a twin breaker in your electric panel. As Dusty suggested, if you don't have room for another circuit in the panel, tying into the air conditioner circuit makes some sense as you generally would not be using both simultaneously.
I think you should be able to microwave and space heat and run the converter simultaneously if the batteries aren't really low and no other significant loads are present. It could be handy to put in a little AC ammeter panel of some sort to monitor your actual current consumption; I have installed one of
these in my motorhome. I did put a low-amperage fuse in where the voltage sense line connects to the 120V system to protect the wires going to the meter in the case of a short circuit somewhere. Some of the EMS units also give a reading of current on their displays.
