Here's what I've done with success:
Turn off the breakers to the converter, microwave, and AC.
Install the 30amp-to-110 dogbone to the umbilical line and plug that into one of the outlets on the inverter.
This will provide 110 power to all of the outlets in the rig. I turn off the AC and microwave breakers just so they aren't accidently turned on when on battery power. The converter also needs to be turned off because you don't want to be using battery power to backfeed into into your battery(ies). Basically, you don't want to use your battery to charge your battery. Not a good thing.
I've done numerous times with zero issues. It's basically the same as running separate outlets that plug directly into the inverter. You still need to be aware of the amperage usage of whatever your plugging into the outlets so as to not drain your battery bank.