The pressure is low, only what it takes to push the fluid through the lines (can't be any higher, it goes to a reservoir at atmospheric pressure).
Probably at most, a few 10's of PSI.
I don't see any reason you couldn't do this. Although, the transmission cooler is way overkill for a power steering setup. I have a little cooler about 3" x 12" for power steering with hydro assist that I bolted in front of all the other radiators, and it's never even beyond warm to the touch.
Whatever you do, just make sure you don't end up making your transmission cooling worse than stock. That'd be a really bad outcome.