What happens if a player plays a unit from hand to Rockfall Path? Is it banished if the player pays for it and commits to the action?

No — nothing is banished. Rockfall Path doesn't allow the play at all, so the action is simply undone: the unit goes back to your hand and the resources you paid are returned.

Playing a unit from hand requires choosing a legal location during finalization. Rockfall Path's "Units can't be played here" is a restriction on that choice, and restrictions on choices must be followed — failure to do so means the card fails to finalize (CR 355.17.b). When finalization fails, the actions taken are undone, any effects those actions caused are treated as never having happened, and the play is cancelled (CR 358.5). So the card returns to the zone it was played from (hand) and the Energy/Power you tapped is un-spent — you don't "commit and lose it."

Note the distinction from effects that instruct you to play a unit there (Temporal Breach, Lillia's token): those aren't illegal plays, they resolve with the play instruction negated, which is how the unit gets banished and stays banished in the Temporal Breach case (FAQ #11673). From hand it's just a cancelled play.