Depends on the prosecutors. On a military base, the JAG officers would usually meet with the prosecutor to determine their best strategy.
That is debatable, however, the clinics still need state approval for the construction, electrical and water hook-ups. They are still, (possibly), covered under the state public health regulations and, definitely, state licensing for doctors/nurses.
Unless they are under a federal government contract to operate on federal property the courts would not find a private entity to be immune from state law.