I have a small cheap heater fan that I use occasionally in my motorhome, mostly to take the chill off in the morning or when parked at home and I'm working on something. Like many here, I would be rather hesitant to leave it running unattended for very long—if only because it's a cheap heater fan and I'm not 100% trusting of its quality and safety.
Your electric fireplace is really just a space heater with a gizmo to project pretty looking flames in the window. If you want to get an idea of how much heat a 1500W electric heater will put out, turn on the fireplace.
Do check to see if the electric plug of an electric heater is warm or hot after a couple minutes of operation. If it's anything more than a tiny bit warm, I'd recommend using a different receptacle as it's clearly not making great contact, causing heating which, if it goes on too far, can lead to a fire.
It's strange that the furnace isn't ducted to the living room area at all, but I guess sometimes RV makers do some really strange things.