An alternative, but incorrect move order

Playing with the black pieces, my friend faced an unusual Blackmar Diemer opening last friday in our teammatch. The move order was as follows : 1.d4 Nf6 2.f3 d5 and now the surprising 3.Nc3!! (diagram)

Play continued 3...Bf5 and a Vienna game appeared after 4.e4 dxe4 5.fxe4 Nxe4 6.Qf3.

Personally, I have never seen this move order, with 3.Nc3 preceding 3.e4 in the Paleface. But can black take advantage of this rather strange move order ? Immediately after the game, I suggested 3...c5 (diagram) and my silicon friend agrees.

The f3 pawn now looks rather silly, unless of course white pulls off 4.e4 anyway. But this seems to give black the advantage after 4.e4 cxd4 5.Qxd4 Nc6 6.Bb5 Bd7 and black is doing great.

So the suggested move order 1.d4 Nf6 2.f3 d5 3.Nc3 is refuted by an immediate c5 as the white f3 pawn is useless.