Yes, known as a dual-fuel system.

Plus 1 on what dadoes and stax said. I might add that auto switch over like stax mentioned is a great feature that;s usually optional so make plans for it when getting estimate.

I'm trying to figure out if an air source heat pump is an option for AC and heat in the fall/spring

If you are looking the save heating costs, then post your gas and electric rates and a calculation can be made to compare the cost to generate the same amount of heat. You will also need to provide the efficiency of the furnace.

As above, it's a fairly common option. You need someone who knows what they are doing to install it. The system needs to turn off the heatpump when the gas backup kicks in (unlike resistance strip backup heat). Unless your electricity is cheap, it's probably not worth the additional cost. It shouldn't cost that much more for a reversing valve and a defrost board but it invariably does!