Thanks for the replies. I agree that, if I'm already on somebody's radar, a traditional position report would make more sense (or even no report at all, in theory, under SSR and squawking 7700).
Outside radar coverage though, I think GPS co-ords would provide much valuable information to the search & rescue guys, provided they are communicated without ambiguity (minutes/seconds vs. decimal etc.) By the way, I didn't know about the different reference frames; I've noticed that my Garmin defaults to WGS84; are there other frames in use in the GA/civil aviation world?
On a slightly drifting note: say that I am in distress in a remote area and only manage to read out my GPS co-ordinates once, at the speed of sound, i.e. the poor guy at the other end doesn't manage to write them down. How easy is it for you guys to play back the tapes on which, I'm assuming, the transmission has been recorded? Can you do it at the touch of a button or is it something you normally leave to the air crash investigators, when they ask for it? Just out of curiosity...