Well, Teslas (and presumably other all-electric cars) have A/C so it's not impossible, but A/C takes a fair amount of power.
On the other hand, Teslas store a lot of energy. The A/C is something like 2.4kW which is about 8,000 BTU/h or about 3HP. So using an electric motor on a conventional car might give you a few more HP briefly, but the alternator has to eventually make up the deficit, and a bit more for its own inefficiencies.
An easier approach would be to drop the A/C clutch out when you tromp on the accelerator. That might allow you to use a smaller engine for the same performance (passing especially) with a simple software change. Probably cars already do that. The A/C would run a bit more after you do that, to keep the cabin air temperature down. No free lunch.
You could always do it with a window air conditioner and a huge inverter, but the efficiency would be pretty bad I bet. The aerodynamics in the below example are also a bit dubious. In a pickup it might actually make sense=- put it in the bed- since a cheap Chinese window A/C is almost free.
