If you are an unbaptized publisher and go in service every week are you allowed to do whatever you please as long as you don't get baptized? Can you run for political office and still comment at the meetings and still go out in service? Wouldn't the society distance themselves from you if you are doing things contrary to their beliefs. Identifying yourself as a JW makes you in all intents and purposes a JW.
In a normal situation you would no longer qualify as an unbaptised publisher.
For Serena Williams I would question what access the society has to her. Prince attended meetings, assemblies and had personal contact with an elder - Larry Graham. He was seemingly on the books of the local congregation.
I don't know about SW but I sincerely doubt that she is on the books of any congregation as an active Witness (unbaptised or not). Even if some old congregation somewhere has her records from her youth I doubt that she has regular contact with Witnesses "in good standing", especially elders. I'd be amazed if she puts a report in.
If she wants to identify as a Witness then that's up to her. What influence she allows the organisation to have on her is also up to her. There is very little the organisation can do about it.