Although the converter and the 120V circuitry, breakers, etc. commonly share a single spot in the trailer, they are two distinctly different units under the hood.
Typically the only interconnection between the two is where the converter power source wires run to the 120 V side and draw power for the converter.
On my trailer the converter is wired to the same circuit breaker as almost every since receptacle in the trailer, with the exception of the one that the microwave is plugged into in the cabinet, and the one outside GFI plug...so when that breaker is off, so is the converted.
As part of my modifications try to get my air conditioner to run on a smaller generator that I owned at one point, I actually installed a toggle switch next to the converter that allows me to shut it off without having to cut power to all the other receptacles in the trailer. Although I don't think that's necessary in your case, it is an option if you find out that the converter is somehow hardwired in such a way that turning breakers off won't kill the power to it.
