Impressive queen sac

No, he can save his queen, but at the cost of his king. For example:
20. ... Qc5
21. Nf5 Kg8
22. Nh6#
To save his king, interposing with the knight seems like it would delay mate the longest.
(a 15 min game I played last night). I had hung two pawns early in the game so the sacrifice was the only way I was trying to break through with either the capture of the e f or g pawns but my opponent protected against the e and f pawn sacs nicely. Fortunately for me she missed the h pawn.
A short game I ran across on chessgames.com, with a really genius ending. White threatens mate with 21. Nf5+ Kg8 22. Nh6#.