That's correct. Winning the pawn both wins a pawn, and critically weakens white's dark squares. Without that, black might not have quite enough.
And I think I change my mind about ...f6 being the best move, after looking at the game explorer (on black's 9th move there were a few master games played), and now ...a4! looks best, taking b3 from the knight first. It seems that after I played ...f6 white should have, after exf6, Nb3! when after ...Bd6 white can get in Be3 with decent control over the central dark squares. If black just plays ...e5, I think (I'm too lazy to put this on a board right now!), white can play Nxc5 Qxc5 Re1!, when ...e4 isn't really a threat. Or maybe I'm missing something. It seemed like this was white's best bet, and though I don't know how perfect the master game with Nb3 was white did win the game. I totally missed that.
Here is a nice example of how well black can liberate himself if white plays the french carelessly.