Anything can be done BUT the conversion is cost prohibitive. Just buy a heat pump since overall it will be cheaper to buy a new one rather than to try and convert a A/C unit to one.

I have a quote for a hybrid heat pump at $6700, I estimate the components and labor to convert my gas pack to a hybrid heat pump around $1900. I also am a conservationist and don't like to throw away good equipment or even components

Good luck and have fun doing your conversion.