Cold air from A/C into Air intake system.

Not really. The colder air will increase power a little, but not enough to offset the losses of running the A/C in the first place.
There is a reason that many performance cars don’t have A/C, and many remove the power steering as well, and that reason is parasitic losses. The less power you use to run other stuff like hydraulic pumps, the more power you have going to the drive wheels. Not to mention the weight savings.

Slightly, but not worth the trouble and possible dirt-entering-engine consequences.