Ehhhh.
I don't disagree for a second that, say, Starbucks could take a hit, reduce profits and still be able to operate successfully in New York. But I'd argue a lot of what makes New York the city it is is things like small independent restaurants that already operate on very thin margins. They also have no fat cat executives pocketing the spoils.
So, perhaps, yes, the city could survive without increasing wages but I worry it would result in a very faceless city filled with nothing other than big corporate entities that are able to swallow the cost.