It's no problem running a heat pump off of solar and batteries. About the only thing you have to watch out for is the startup current surge for a unit with fixed speed compressor(s). Single and two speed units that have one or two fixed speed compressor(s) with have a very high startup current. So, you have to make sure the inverter can supply that much current. If you use a unit with a variable speed compressor, then you don't have to worry about that and they are much better units anyway, so I'd recommend that approach. Pretty much any minisplit will have a variable speed compressor. In more traditional split systems, with an outside condensor unit and an inside air handler, some new models will have variable speed compressor, but many will have fixed speed compressors.