Lemme clean this up:
If you are refering to in battles, yes.
Darmanitan can learn Psychic and Rest which are both Psychic moves, and if your Darmanitan's Hidden Power type is Psychic, that would be included as well. However, Darmanitan reverts to its normal self after battle, therefore it can't learn any moves that normal Darmanttan can't. So that also ends up as a no.
So, the Normal Darmanitan can learn 3 Psychic moves, and in Zen mode, other than STAB, Darmanitan gaind no "psychic extra powers" whatsoever...