Nope, Fallout 1,2,3,NV all have quite different stories. They are infact set in the same timeline (During Nuclear war) but the previous installment's story doesnt continue into the next one except few narrative phrases said by some NPC's. The game is one of the finest games ever created. It's a masterpiece. FO3 already won game of the year before. FO and Elder Scrolls set new standards high in RPG genre.
Since it's a SP game, I'm gonna torrent it
but the nostalgia feeling of playing FO4 after waiting quite a long time for it , is pretty exciting