It’s a reasonable plan. It demonstrates your interest and commitment. I hope you are planning to apply to more than one B school. Stern is great, of course, but there are many other good ones within a couple of hours of NYC. In my city Wharton is, of course, one of the top ten in the nation, but there is also Temple, which is very good, as well, although not top ten. Think about where else you might want to go. Don’t put all your eggs in one baseball cap.