Again, there are several accents associated with NYC. Linguists like to believe that there's one New York dialect called, not surprisingly, the New York Dialect. However, a trip around NYC will tell a different story. You've got everything from the old school(and slowly dying) "Brooklynese"(a good example being the voice actor of Joe from Mafia II) to the Puerto-Rican influenced accents of Spanish Harlem and everything in between.
50 Cent, who by the way, has never pronounced his name "fitty"(watch any Youtube clip of him, EVER) has what is known as the African American Vernacular English accent, with a little New Yahk thrown in the mix. It doesn't sound much like what most people associate with the New York Dialect. This is because the Great Migration(basically when the blacks moved to the cities from the South) occurred largely after the influx of Jewish and Italian American immigrants into NYC(which contributed most to the New York Dialect). Well, about a million or so moved to the big cities in the 1920s and 30s, but the largest migrations happened 2-3 decades later, after the apex of Jewish/Italian immigration.
Which is a long-winded and pretentious way of answering The Mad Dooby's question: yes, technically 50 Cent does have a New York City accent.