This is exactly what I did a couple of RV's ago. My inverter had a transfer switch build in as well as a battery charger. I found the breaker to the refrigerator outlet and spliced my inverter into it between the breaker and the fridge. at the same time I disconnected the dc converter because the inverter was a charger also, I didn't need 2 charging the batteries at the same time. I also added a battery. I had 24 hours of power for the refrigerator AFTER it was cold. so it wasn't required to run the generator while we weren't plugged in. without the transfer switch built in the inverter, it would have been much harder to do.
Modified sine wave worked fine for me, laptop, tv, fridge, I haven't found anything it won't work on yet.