In Punta Cana or in Bavaro?
In Bavaro hotels, you have both Orange and Verizon. In some rooms/location the signal quality may be weak, but in general, both Orange and CLARO (no longer Verizon) have coverage there.
If you are referring to U.S. Verizon Wireless, yes they have coverage, through a roaming agreement, most probably with CLARO or Centennial.