Jeremy,
The Hurricane heater does not have a 120V heating element in it. However there are a large number of coaches that were equipped with Hurricane heaters that had an aftermarket Comfort Hot back-up electric heater by Rixen's Enterprises, installed inline with the Hurricane. With the Comfort Hot system you can heat the coach on shore power using the floor heaters with the outside temperature below 20 degrees without running the Hurricane burner if you are on 50 amp power.
The Patriots that were the first to have Hurricane heaters installed, did not even have an electric domestic water heater, so a lot of them had the Comfort Hot systems installed because they had to leave the Hurricane burner turned on year round to heat their domestic water without it.
So the answer to your question is, no you can not heat the coach on shore power unless your coach has had a Comfort Hot system added to it.
Gerald