The exception, if I'm interpreting the Code correctly, is when a 125-volt, 15 or 20-amp receptacle is not used. Either hard-wiring it, (no receptacle at all) or using something different. I suppose a NEMA 14-15R (125/250-volt, 3-pole, 4-wire) would not require a GFCI, even if it were supplied with only a 120-volt circuit.
Upon further reflection:
I don't think I've ever seen a NEMA 14-15R, except on a catalog page.
It's no more work to hard-wire a garage-door opener than to change the cord.
Will a NEMA 6-15P (250-volt, 2-pole, three-wire, without noodle) fit into a NEMA 14-15R?