I agree with Stephen's points however...
... in normal times, with no previous repetition, Qç2
is actually a good try to win the game!
The plan to win this game is to bring the Black King to g3 in order to mate the White King. Meanwhile Black should protect the b7-pawn, which will be attacked by the Bg4-c8 maneuver.
First, I didn't see how White defends against Black's plan because in practice it is very hard to defend this position. Here is an illustration:
[fen "8/1p2k2p/1Pp5/2PpNq1P/3P4/4PB2/4K3/8 b - - 0 1"]
1... Qc2! 2.Ke1 Kf6! 3.Bg4! {the best idea to draw the game} Qg2! (3...Kg5 4.Bc8 Kxh5 5.Bxb7=) 4.Bc8 Qg7 5.Bg4? (5.Kd2 Kg5 6.Nd3!! {see the following diagram}) Kg5 6.Ke2 Kh4 7.Kf2 Qf8 8.Kg2 Qf6 9.Bf3 (9.Bc8 Kxh5 10.Bxb7 Qg7-+) Qg5 10.Kf2 Qg3 11.Ke2 Qh2 12.Kd3 Qb2 13.Bg4 (13.e4 {is not so effective} Qb3 14.Ke2 Qc3! 15.exd5 Qxd4 16.Nxc6 {sets a nice trap} bxc6 17.dxc6 Kg3! (17...Qxc5 18.c7=)18.c7 Qf2-+) Kg3! 14.Bc8 Kf2 15.Bxb7 Ke1-+ {and the mate follows soon} 16.Nf3 Kd1 17.Bxc6 Qb3#
Now, I am not so sure it's winning because White has a fantastic fortress, which consists of transferring the Knight to f4, via d3, to prevent the Black King to enter.
[fen "2B5/1p4qp/1Pp2k2/2PpN2P/3P4/4P3/8/4K3 w - - 7 5"]
1.Kd2 Kg5 2.Nd3!! Kxh5 3.Nf4 Kh4 4.Ke2 Qe7 (4...Kg3?? 5.Nh5) 5.Kf3 {and the Black king cannot enter into g3!}
Black can improve its position by pushing the pawn to h4, bringing the King back to d8 to chase the Bishop and centralizing the Queen. It can also set some traps. It's horrible to defend for White, but I am not sure this is a forced win.
[fen "3k4/1p6/1Pp5/2Pp4/3PqN1p/4P2B/5K2/8 b - - 75 49"]
1... Qc2 2.Kf3 Qh2 3.Bg2?? (3.Bf5 {and I don't see a clear win}) Qg3 4.Ke2 Qxg2!! 5.Nxg2 h3-+
To capture the h5-pawn is probably not useful because the h7-pawn can go until h4 and then it is stopped. Moreover, the h4-pawn prevents the Black King from entering. However, so far I have not been able to find another winning plan for Black! But, I'm trying...
[fen "2B5/1p4qp/1Pp5/2Pp2kP/3P4/3NP3/4K3/8 b - - 10 6"]
1... Kh4!? 2. Nf4 Kg3 3.Nd3! {the Knight is a super defender} Qf7 4.Kd2! Qe7 5.Ke2! {to close the door for the King}