I've always wondered- would you be able to fish off of one of those rigs? And, don't they have a desalination setup on those? Seems an awful lot of weight to ferry out there as potable water, when you're surrounded by water.
KnightoftheRoc, some of the newer ones can. But in the North Sea, most of the Rigs are 20+ years old Jack-Ups, immobile, and require constant support from onshore. The rig floor's over 100ft above sea level, making fishing more or less impossible. And with over 50 people on board, a solitory haddoc isn't going to go far. Saying that, there's a few long haired Rough necks on-board most rigs; maybe one of them's Jesus...
And unfortunately, the survival time in the North Sea, even in the survival suits we have, is a matter of minutes not hours. We'd freeze to death or drown before we could get rescued.
I'd say our best bet, as long as everyone stays calm, is to fill a life boat and head for nearest land. Once the boat's sealed up, it's pretty water tight. The problem is that they're like a bottle; once opened, if the crew don't dissembark properly (i.e, they panick and don't distribute their combined body weight/balas properly) then the boat will capsize very quickly and with only one exit, drown the crew. So in a time critical SHTF situation, with panic, anger and fear riding high, this would be a bloody frightening move.
On a drill ship,or floater, we could at least make our own way on board the vessel. Would be relatively slow, but we'd be in more control.