Smashing post - very instructive things here.
White to play.
He played 19.g3 a very handy waiting move using the c3 pawn as bait.
So you had this position in front of you before pressed 'Send Move'.
Most non mating combinations involve an unprotected piece.
Here you have the advantage of seeing what the position will be before
you play the move.
I've been advising a 'pre send ritual' where before you send your move
you scan the board looking for unprotected pieces to see if there is any
way either side can profit from this.
The Black Rook on c3 is flashing like a beacon 'Look at me - look at me"
And then, as Philidor correctly noted: White screwed it up
Instead of 20.Rxe8+ he should have played 20.Qg4+ Kf8 21.Qd4
Hits the unprotected c3 Rook and mate on h8. No defence.
So to answer your question - yes after White messed it up 21...Kf8 would draw .
If you had done a pre-send ritual you would have spotted this.
You were looking at this very position when you pressed send.
You admit you made the blunder - good. Learn from this lose.
The game itself was a bit sloppy by Black - the other lads are
offering some good advice here
But you must wipe out the tactical flaws first.
It's a jungle out there Lousey, they will eat you alive if cannot spot
and handle the two move trick or a basic Queen fork.
White may have thought it did not matter about the move order
so played his combination 'ass about face' thinking he had 22.Qf6 in this postion.
Which is the same idea but not correct - Black holds with 22...Qe5.
So today's lesson:
Look out for those unprotected pieces.
Always check your move order when playing a combo - it matters.
Thanks again for the post Lausey.
Here is how the game should gone after Black grabs the c3 pawn.