I was thinking about getting this pump, but have a question.
Can I use this at the track like the electric water pump I use to cool the coolant quickly with the engine off for hot laps at the drag strip. Will it still pump with the engine not running?

 

The whole point of that is to pump with the engine not running, while the car is being towed.
I guess if you could rig it to work with a fan mounted trans cooler running at the same time it might do something.

 

I'm no trans guru, but I would think the electric pump would have a hard time pulling through the trans pump and valve body. I'm just guessing.

 

Those things are made to install on cars that get pulled behind motorhomes a lot. That pump circulates fluid as it would if the engine was running and prevents the trans from damage due to no lube.

In the OP's idea, it would either work or not for cooling, if it didn't he would just be out the money of the pump.