The old original Dexron and a few of it's successors make pretty good hydraulic fluid. If you think about it, what is going on in a auto trans??? Oil is being supplied to pistons to squeeze the clutch packs. It lubricates gears and roller bearings as well a bushings. JUST like a power steering system. My skid steer loader uses Dexron in its drive system. IIRC there is 20 gallon of it in there! The Hydro-stat in my garden tractor recommends Ford Type 1 fluid or an approved hydraulic fluid like the big tractors use.
MY OPINION, Use some tranny fluid. It will be just fine in the PS system. You could probably go to Tractor Supply and buy some THF (trans hydraulic fluid) and put that in the PS system without concern.
Ken
EDIT: If all I had was Dexron and I needed 3 quarts of oil to get me 5 miles home, I'd dump it in the engine. Of course I'd change ASAP after I got home but the point is it will lubricate just fine.