Yes, most people here agree that you should resign in a completely hopeless position. But about the "GOOD GAME" part... you should definitely check a few of the threads here that are related to the topic. They shouldn't be too hard to find.
Surrendering? A show of respect?
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It has been 15 years sense I actively played. Just started playing again and have been playing here or a few weeks, when did it become never surrender chess. I was always taught from a very early age that surrendering was to show respect to your opponent and was never a bad thing. I am not talking about being down an exchange or a piece but when you are beat just say GOOD GAME and surrender. Don't wait the 2 or 3 days and let time run out just to be a jerk or same thing in a tournament when you have lost surrender. Show respect to the better player and learn from them. I always try to play better players because that is how I learn look at my game history and can see I am not a great player but I love the challenge. I always show respect to my opponent and that is the way chess should be.