Well, the delay finally happened to us. Needed to transfer P2's UR to TrueBlue (more than 100k worth of points), and it did not happen instantly. Ended up taking around 26 hours. Luckily the award ticket was still there, but sure was nerve wrecking.
FWIW, this was a large chunk of points, and P2 have never transferred any UR points before (we've been saving them with the Chase trifecta), so that probably is what tripped it.