Yes.
As long as there is more the one outlet on a branch circuit 15 amp devices are allowed on 20 amp circuits.

If you had a single receptacle on a 20 amp circuit (and no other outlets) it would need to be 20 amps.

That's some amusing side-stepping in the NEC... I smell lobbyists, lol.

To be clear though, ALL the conductors on that 20A branch would need to be AWG12 (if Cu) or larger, right? You can't have, say, 12 ga. from breaker to first box w/ 20A rated receptacle, then AWG14 from there to a ceiling fan, right?

No lobbying involved, just basic practicality. You are correct in that you can't have lower ampacity wire on the circuit than the OCD (in the typical case). However, 15A receptacles are rated to be on 20A circuits.

The rule is that if you have ONE receptacle on a circuit, the pin configuration must match the OCD. A 30A breaker must have a 30 A receptacle (can't have a larger or smaller.

Just a note on the reasoning.

If you have a "normal" branch circuit with multiple outlets, you can use the 15A receptacle. This is the majority of the wiring you'll find in a home. Basically, when you have multiple receptacles with a total load of less than 20A, no single receptacle is going to require more than 15A.

If you have a dedicated circuit where there is only going to be 1 receptacle, then you need to use 20A. The appliance (or whatever 1 item) needs 20A available, so it all has to be able to flow through that receptacle.

No matter what, the wires need to be able to carry the full 20A safely.