What you’re doing is really no different than a fan. Colder air but less volume. That fan I have moves about a million cubic ft of air. Hot air but a lot of it. We use to cool down the seating area under the canopy when not cooling the motor. What I won’t do is put ice bags on the SC. Expensive lesson for me on the dyno.
That's a nice fan, for me, poor boy racing, I would like a battery operated stand alone fan where I wouldn't need a generator, not sure if there's one like that though, will have to check.
What I did do for a while is, rig wires & plug off the battery connection under the hood, & plugged in a 16" radiator fan to sit on top of the s/c & front of engine, but it runs down the battery too quick & with the oem fans running in cool down mode.