I guess the bigger question is, will subways have as much demand once self-driving cars become big? Obviously, no, if the cost for hailing a self-driving car becomes almost as inexpensive as a subway. But there are things the city of New York could do to impact that, such as reduce street capacity (i.e. increasing pedestrian and bike capacity).
But that's just New York. Everywhere else in the U.S. where mass transit is not a daily option, automated cars will be a daily habit. Inevitably, as more and more people migrate to New York and expect automated cars to be the default option, it's hard to imagine subways (and buses) winning out, absent some major limitation in self-driving car production or capability.
New York will always be an anomaly...but yes, I'd have to agree with your speculation that suburban living would become much more attractive without having to worry about car ownership or driving. And this would most definitely impact commuters to New York. But if self-driving cars become a ubiquitous option, will there be the political appetite to continue subsidizing mass transit rail, such as the kind that is currently used to bring in upstate workers to the city today?