According to Colson Whitehead, yes. As he professed in his collection of essays, The Colossus of New York:

No matter how long you have been here, you are a New Yorker the first time you say, That used to be Munsey's, or That used to be the Tic Toc Lounge.

I've done that now, but I am beginning to consider myself a New Yorker for other reasons. The newest one is that I now subscribe to the three big "New York" magazines -- New York, The New Yorker and Time Out New York. Each week I spend most of my reading time working through these three publications. My recent desire to take a break from fiction is part of the cause, but the choice to subscribe is a bit bigger than that.

Truly, I think it stems from my recent decision to renew the lease on my apartment and commit to staying in New York for another year. Up until now, I hadn't committed to staying here for any definite amount of time. I've only really lived in sublets up until this point. My new commitment inspired a barage of purchases at Ikea and Crate and Barrell, as well as these new magazine subscriptions.

Thinking about it all, it seems I've always been a New Yorker and I'm only now admitting it to myself. The only thing I'm nervous about now is when I actually have to leave.