If a bird is fed whilst on deck then that does prevent its inclusion onto the British List as it is deemed to have arrived with human assistance rather than in a natural state, but the simple act of landing on board a ship is deemed ok as its no different to landing on a piece of flotsam to survive and maybe recover some strength. If a bird is fed on a ship then this is viewed as interfering in its natural migration as it may not have survived the journey without that food so in effect arrived here artificially.
Obviously in many cases we probably wouldn't actually know if a bird had or hadn't hitched some, or most of the way, by boat, or whether it had been fed or not if it had, although there are instances where we are aware of such circumstances such as the Catbird that arrived in Southampton on the QEII having been fed during the journey (and which even stayed on board and subsequently toured the Med!), and the Snowy Sheathbill that was brought back to Plymouth from the Falklands and which in addition to being fed, I think had even been taken below deck!
There is undoubtedly a good number of birds that land on ships in the Atlantic, especially near to the eastern seaboard of the States, but as to the percentage of vagrants that survive a crossing that way and arrive here would be guesswork, but certainly as already mentioned species such as Sparrows are far more able to make the crossing that way than insectivourous species, and the location of landfall such as Seaforth (Song Sparrow & Blackpoll Warbler) and Landguard (Lark Sparrow) etc is another clue to their potential method of arrival.
I remember being shown a dead American Robin at Felixstowe Docks once which had been found on a container boat which was pretty galling as I still needed it at the time and had even been all the way to Scotland (Inverbervie) and failed to see one!
Simon
Edit: In 1986 the BOU amended the definitions regarding ship-assisted vargrants that were barred from Cat A from birds 'which have certainly arrived with ship assistance' to birds which 'certainly arrived with a combination of ship and human assistance, including the provision of food and shelter'