I did that with an inverter off the 12VDC (my three way decided to become a
two way, it was cheaper), so I didn't have to run the gen or fill the propne
tank. The inverter kicks in when there is no AC voltage (from shore power),
and always either passed thru or gave 110. I did have to add another module
to the inverter that cut it off when the DC voltage dropped too low
(assuming the engine wouldn't start), but to me that was no worse than
having the gen gas pickup cut off the gen when the gas gets low so you can
still start the RV.

I installed a dedicated inverter to run the 2-way fridge while travelling.  It
powers up when the engine is running and there is no other source of 115 VAC.
The alternator can easily handle the load, and we use no propane while
travelling.  As a matter of fact, I usually have the propane shut off at the
tank during travel.

Paul

IMO a lot depends upon why you want to make this conversion.  From a purely
economic standpoint it doesn't make much sense.

I have a 3-way frig and on DC, uses 16A and the DC operation is the lowest power
input but also the lowest cooling.  I would suspect that running a converter to
run the AC you would be using close to 20A when operating.  Does you alt have
that much power to spare?  As for propane, it uses very little gas.  Takes about
1.5 weeks/gal if running FULL time.  More realistic est is 3-6 weeks/gal
depending upon duty cycle which is very much related to weather.

If you have a fear of the propane being on while traveling, maybe the cost is
justified if your alt can handle the additional load.

Mickey

Many people say that if you must replace a refrigerator that a
compressor type refrigerator (110V) may be your wisest choice.

They are much less expensive than propane capable fridges, they are
usually more energy efficient, and they have much greater cooling
power (you can make ice quickly.)

I have a 110V compressor type fridge & am pleased with it. The biggest
limitation is that one can't drycamp for long without recharging the
batteries.  If you seldom camp without electric that's no problem.