Is this really playable ?

I was gettng some feedback on the "The Bouver gambit" in the Vienna defense from a friend. Instead of the regular continuation 5.g4 Bg6 6.g5 Nd5 7.Nxe4 Nc6 8.c4 Ndb4 9.a3 Qxd4 10.axb4 he suggested 9.a3 Bxe4 10.fxe4 Qxd4

White's pawn centre is a complete mess, and resembles the play of a chess novice. Furthermore, white has not yet captured the piece and is even a pawn behind. So could white survive this ? Let's look at the possibilities after 11.Qe2.

It seems that 11...000 is a great black move. It sacrifies a piece, but develops the rook. White must waste a tempo to capture the knight, but has no other options ( 12.Bh3 is also suggested, but white has to capture anyway after 12...e6, so the immediate 12.axb4 is more flexible ).

After 11.Qe2 000 12.axb4, Houdini believes that the only good black move is 12...e6, releasing the black squared bishop ( 12...e5 allows white one developing move with 13.Bh3+ Kb8 and now 14.b5 wins ).

Houdini now suggests 13.Bh3 or Be3, both with equality. Let's look a little further on 13.Be3

a/ 13...Bxb4+ 14.Kf2 Qxe4 15.Nf3

Black has several moves here to continue the attack against the white king. Opening the g and/or h-file with the simple 15...h6 seems most promising, eg 16.gxh6 gxh6 17.Rg1 (=)
White's king has found some shelter and the resulting position is highly uncertain, with black having the attack ( but without a clear refutation )

b/ 13...Qxe4 14.Bg2 ( 14.Nf3 as above allows for Nxb4 )
...b1/ 14...Qf5 15.c5 Nxb4 16.Qb5 (=)
...b2/ 14...Bxb4+ 15.Kf2
......b2a/ 15...Qf5+ 16.Nf3 (=)
......b2a/ 15...Qh4+ 16.Kf1 (+=)

So it seems the white monarch can find some temporary support behind his pieces. But this might not be sufficient to survive in the long run...