I tried that for fun and it does work, but the converter will cause the inverter to draw about 6 amps from the batteries. So the solar will have to make up for that, as well as whatever other amp draw there is by the inverter running other 120v things.
You do need a solar controller between the batteries and the panels.
The inverter then runs off those batteries and powers all 120v items, including the converter. The converter can then make your 12v for all those systems. There is no "loop" converter/inverter to worry about as such.
It depends very much on how much sun you get and how much DC you use for how much of a battery bank runs the inverter etc etc, but it is doable in certain scenarios.
Best to have a portable generator and a good battery charger in case not enough sunshine sometimes.
Your converter in that old rig can run the 12v things, but might need a battery to act as a filter for its dirty DC, but perhaps not--it depends if any of the 12v things need clean DC. Also the converter will be a poor battery charger for any house battery you do have.
You could use a new type deck mount converter as your battery charger to go with the portable generator. That converter could also be used instead of your original one to do things either way--house battery or not.
You will be missing any alternator charging of the house battery if there is any set-up for that in that rig.
If it has a generator, note that many rigs have it so the generator needs the house battery for starting it.
