Hi there,
While I do find this highly unlikely, it doesn't hurt to ask when the time comes. That said, you will have to provide a very real/serious reason (generally family).
Despite the "exodus" that is happening in New York, I do think your odds are very low. Your best bet is to temper expectations in terms of an immediate transfer.
Now, when you do join, here's the best way to optimize your chances of getting a transfer 1-2 years in
1) Build a stellar reputation - do good work, work hard, and be known as "the guy/gal" for xx
2) Build your network - network agressively (yes, networking doesn't end once you've gotten the job offer). Make sure you're known by and have allies in people who make decisions such as staffing managers, Partners (specifically those responsible for recruiting/resources and who are heads of industry/function verticals), etc.
2) b). When I say network "aggressively" please don't be needy/annoying :) There's nothing worse than someone who is obviously working the room or trying to please!
3) Look out for opportunities - as mentioned in this Q&A already, look for office transfers, short-term projects, ambassadorships, etc.)
4) Practice patience and be flexible - how long have you tried for? This might take a year. And you need to be ready to go at the flip of a coin.