The North Atlantic Current is actually weaker than the Gulf Stream. Bodies being carried by them would have become so water logged and decayed that they would have sunk into the ocean. Wreckage, perhaps small pieces. Wood would have rotted or become so water logged that it would have sunk just like the bodies.
The current, however, might have made it more difficult for the survivors to swim around and stay afloat. They already had several counts against them as it was. If you've ever been in ocean water with from 8 feet - 2.5 miles between your feet and the bottom, you'd know that just staying afloat can be tiring. Lifevests aside, if you're in water so cold it will kill you in 10-15 minutes, you've swam very little in your entire life and are laden with thick, water-logged clothes, you're going to get exhausted in a bleedin' hurry. Add the current and you'll only die faster.