Playing the Jerome Gambit - or any other opening, as far as I am concerned - in bullet (1 minute, no increment) chess is madness; but, as the following game from lichess.org shows, as was said by Hamlet, "Though this be madness, yet there is method in 't"
obamaGANDON - JAVAD76
1 0 bullet, lichess.org, 2014
1.e4 e5 2.Bc4 Bc5 3.Bxf7+ Kxf7
Listed in lichess as "Bishop's Opening, Jerome Gambit" but referred to on this site as the "Abrahams Jerome Gambit". For a recent discussion, see "Alert!"
One advantage for the attacker in bullet chess is if the defender does not know the best opening moves, the game can be over very quickly due to an early blunder. Here, for example, Black's best move is 4...Kf8, with an advantage.
On the other hand, this is a bullet game, and anything can happen.
The only other game that I have with this line in The Database continued 5...Qe7 6.Qxh8 Qxe4+ 7.Ne2 Qxg2 8.Qxh7+ Kf8 9.Rf1 d6 10.d4 Bxd4 11.Nxd4 Qe4+ 12.Ne2 Bg4 13.Nbc3 Qxc2 14.Bh6+ Nxh6 15.Qxh6+ Kg8 16.Qxg6+ Qxg6 17.Rg1 Nd7 18.h3 Re8 19.Rxg4 Kf7 20.Rxg6 Kxg6 21.Nd5 Ne5 22.Nxc7 b5 23.Nxb5 a5 24.Nxd6 Re6 25.Nf4+ Black resigned, burraburra - grechy, FICS, 2011.
Best, according to Houdini, is 5...Bxf2+ (getting a pawn for the endangered piece) 6.Kxf2 Nf6 when White has an edge, a pawn up.
With the text, Black may be remembering the Blackburne Defense to the regular Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.Nxe5+ Nxe5 6.Qh5+ g6 7.Qxe5 d6) but the Rook sacrifice does not work here.
Up the exchange and two pawns, White "only" has to make normal moves and watch his clock.
6.Qxh8 Be6 7.Nf3 d5 8.Qxh7+ Kf8 9.Qxg6 Bf7 10.Qf5 Nh6 11.Qf4 Ng8 12.exd5 c6 13.0-0 cxd5 14.Ne5 Black forfeited on time