Are former members of the uniformed Public Health Service and National Oceanic and Atmospheric Administration considered to be veterans?

Everything that I have found in regards to Public Health Services, specifically United States Public Health Service Commissioned Corps, the USPHCC is considered Federal Uniform and therefore can claim Veteran status, per 42 US Code Chapter 1

One of my neighbors is retired from the PHS, she has a blue retiree ID card. She is considered a military retiree and the rank listed on her ID is, I believe Captain (Navy type). Her military benefits appear to be no different than any other veteran.

According to U.S. Code of Federal Regulations, "Veteran" means a person who served in the active military, naval, or air service and who was discharged or released under conditions other than dishonorable. The regulation further specifies that "Armed Forces" means the United States Army, Navy, Marine Corps, Air Force, and Coast Guard, including their Reserve components.
With this in mind, I would think the answer to your question is "no."
Edit: I expect that following the creation of the Space Force, 38 CFR will subsequently be updated to include them in this definition.