Applying to a school with a new PhD program
Georgetown and the University of Maryland have new PhD programs in
  biostatistics


Even though the program is new, both of these are very reputable universities. It is the same faculty, same resources, and probably same philosophy. Therefore, no risk there in terms of program age.


  More specifically, does that hinder future employment because the
  university doesn't have as many connections with other places? Does
  the fact that these universities already had a masters program
  mitigate that?


I don't think it matters. What matters for future employment is what you learned, new skills and experience gained, leadership development, goal oriented personality, and ability to work in teams.