I've used synthetic ATF in my GM power steering systems for years. No issues so far.
But I did have two pump failures on the same vehicle while using approved power steering fluid. The first failed for no apparent reason... just didn't work one morning. This was on a '94 Chevy Corsica- 6 years old and 80k miles at the time.
The second was a heat failure. This involved a 110 degree day, a STEADY 50mph wind from the South (in BFE Kansas), driving west at 80mph in a construction zone with the lane tilted HEAVILY to the north. This situation required the p/s pump to put out pressure for probably an hour... when it was already hot as [censored] out. It boiled the fluid, puked it all over the belt... allowing the water pump to slip, resulting in an overheated engine. This was on a Sunday afternoon in Goodland KS. There's almost NOTHING in Goodland KS anyhow... and none of it is open on a Sunday afternoon. I wiped off the belt, filled the p/s with 10w30 motor oil (the only petroleum-based lubricant available at the one run-down gas station that was open), and limped the car home 180 miles across the barren wastes of Eastern Colorado... at 50mph with a growling p/s pump.
The fix involved a thorough p/s flush, new pump, a magnet in the reservoir to catch remaining metal, ran the p/s return line through a small transmission cooler, and filled the system with Mobil 1 synthetic ATF (has since been turkey-baster flushed on occasion with Mobil 1, DexVI, or Transynd, depending on what I have on hand). 9 years later, I'm still getting metal off that magnet (though very little these days), but the system has been trouble-free since.