It does not - Black has an in-between capture with 1. ... Rxc3. Still after his own in-between move, 2.Rxf7 Kxf7 3.bxc3, White should win -- not because of his extra but weak queenside pawn, but thanks to his potential outside passed pawn on the g-file.
The game might continue 3. ... b5 4.Kf2 Kf6 5.Kf3 Kf5 6.g4+ Ke5 7.h4 h6 8.Ke3.
White will create a passed g pawn and then exchange it for Black's passed e pawn. At that point White's King will be much closer to the queenside pawns than Black's King, so White will win.
Doesn't 1.Rf6 Kxf6 2.Ne4+ win a piece?