This is the stuff that aggravates the living $h1t out of me with some of the current Active Duty Nukes.
I've been retired almost 2 years, so I am not as in the loop as I was before. However, I spent 30 seconds doing a Google search for Navy COOL then another 30 seconds picking Nuclear ET. The result?
https://www.cool.navy.mil/enlisted/et_nuc.htmAnother 20 seconds to open the "Other licenses" tab near the bottom of the page, which has this link
https://www.cool.navy.mil/search/CERT_NFO2994.htm that clearly states:
"NRC licenses all individuals who either operate or supervise the operation of the controls of a commercially owned nuclear power reactor or a test/research (i.e., non-power) reactor in the United States. Although the regulations in this area generally apply to power, research and test reactors, this site focuses primarily on the operator licensing activities at power reactor facilities. Additional requirements and certifying information is available from the certifying agency's web site."
and:
"The following Navy Enlisted Ratings provide training and/or experience that contributes to attaining this credential:"
Nowhere on any of the pages does it state that any type of license can be obtained through Navy COOL.
Grand total of less than 5 minutes to answer the question that the OP
should be able to answer themselves.
Maybe I'm just getting grumpier the older I get.
End of rant........ for now.