possible. but white gets a huge lead in development after the simple 5. d3 at least if black wants to get his pawn back. fxe4 dxe4 Qxe4 Be2 and unless black throws in Bb4+ which is met with c3 white will castle on the next move and black is in trouble. even after 5.e5, g5 6.d4, g4 7.Ne2, d6 8. f4 and now white has a huge center while black has gaping kingside weaknesses.
new idea an Damian
Sort:
1.e4 e5 2.Nf3 f6 3.Nxe4 Qe7 4.Nf3
and now f5
and on 5.e5 g5
is possible, is not it ?