I think there are a lot of people in NYC (not compared to the size of that city, but a high absolute number) that tune into Syracuse games (especially basketball) and you could probably consider fans of the team. If Syracuse is capturing even just a tiny fraction of sports fans in NYC, that is still a significant number of people.
I think that looking at the absolute size of the fanbase is kind of misleading though. Maybe Syracuse actually does have more people you could count as fans than Auburn or Tennessee do. I kind of doubt it, but it is possible. Syracuse's fanbase, even though it might be larger in absolute terms, has a fraction of the enthusiasm/passion and spends a fraction of the money.
Plus, Syracuse is a basketball school, so I wouldn't expect them to sell out the Carrier Dome for football games even if it was located in Midtown Manhattan.