Derek Cole explains that an electric resistance furnace can heat your home without a working heat pump compressor, but your electric bill will jump 5 to 7 times higher. A better retrofit for mobile homes: add a heat pump outside and keep the furnace as backup.
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So when you use that backup heat as the main heat, which will happen when your compressor is out, you're gonna have some 5, 6, 7R light bills. It's gonna be quite painful, but it will work. We do a lot of modular homes and mobile homes, and their original setup is air conditioner outside, electric furnace inside. Well, we do. We go back with a heat pump outside and use that electric furnace inside as the backup heat source. That saves them a lot of money, because now your primary heat is the heat pump. Your secondary heat is the electric furnace. So I would never use the secondary as my primary because of light bill reasons. But yes, to answer your question, it will work. Do I recommend it? No, I don't.