Stewart Reuben wrote: I am sure the players want to get away from their horrible positions as quickly as possible.
I can understand that point of view.
A few years ago, after being outplayed by a much weaker opponent, I found myself the exchange and two pawns down without compensation. It was probably resignable, but as I had 30 seconds left to make two moves before the intermediate time control, I decided I might as well bash out a couple of moves and then take stock.
My first move allowed my opponent a mate in one, which I saw as soon as my hand left the piece. My immediate reaction was to resign there and then, but I decided to allow him the satisfaction of making the checkmate move. He had plenty of time left, but after studying the board for a couple of minutes made a different move.
My relief was tempered with irritation that I would now have to play on in what was still a hopeless position. I could have still resigned, but as it was an away match I would have just had to sit around waiting for my team mates to finish, so I played on. From this point on my opponent started to make moves more befitting his lowly grade, and proceeded to first throw away the win, and then 'simplify' into what was a lost ending for him.
So I suppose the answer to the question is 'it depends' - not so much on the position, rather on your confidence in the ability of your opponent.