This has come up before. Not aware that anyone actually tried it on a Solera yet. My memory of the earlier discussion says that about a 400 watt inverter should be sufficient. Also, as it is a heater element, a (cheap) pseudo-sinewave inverter likely will work. If used to maintain temp (NOT to initially cool the fridge down) I suspect it would work okay. As stated above, the fridge uses very little propane. I would consider the advantage to be not having to turn off/on for tunnels or ferries that restrict propane use. None of those I'm aware of around here - though I did have to turn it off for the Alaska Maritime Highway ferries (fridge maintained cold just fine on those segments of our trip - nothing thawed). Moving the plug when camping and disconnecting when wanting to run on propane seems more of a hastle to me than the benefit - couldn't think of an easy "automatic" method to switch among the three sources (12 volt inverted to 120 volt, 120 volt shore power, and propane).
If you do it, let us know how it works out.
2012 Solera "S"
Calif SF Bay Area