Yes. You can definitely do this. Gas heating costs can be tough to beat at lower temps, but above 25 or 30 the mini split is likely a slam dunk and that covers a lot of winter hours. The only trouble is that heat pumps can be kind of expensive and the cost might be tough to justify if you only use it a little.

OTOH, with the new heat pump rebates in the Inflation Reduction Act (IRA), I think it might always make financial sense to go with a high efficiency mini-split heat pump over of a plain mini-split AC. The heat pump rebate should more than cover the additional cost of the upgrade.