Gotti took over an organization that had about 250 made members, so not really "hundreds and hundreds."
According to the FBI the Gambinos had 300 made members in the late 1980s.
That's an army for sure...
Don't forget the at least 2000 associates or more back in the days. Associates are just as important to any family as its soldiers. A mafia family doesn't have to have many made members. When it has a good amount of important associates, it can come a long way.
