Well, since Bette wants to play with counterfactuals (always a tricky business and something that most sensible people avoid), let's play that scenario through:
In Bette's case, the answer would in fact be no, she would not have universal health care. In fact, Bette would never have existed, and her parents would have been consigned to the ovens, if not at Auschwitz, then elsewhere.
Why? Because Bette is jewish - as the wiki article on her
says - and in her alternate universe the United States doesn't exist - the French and the Spanish owned most of North America, with the British having a small slice on the East coast - and therefore the Nazi juggernaut in the West was never stopped in Bette's preferred alternate reality - no United States, with the massive material resources the US brought to the fight against the Nazis, means no effective resistance to the Nazis (or to the Japanese). As such, the UK, and the North American colonies of the British and the French, all became part of the Nazi Third Reich, and therefore subject to the Nazi "final solution."
In other words, in Bette Midler's preferred alternate reality, she doesn't get universal health care, she gets a universal "final solution."
Amazing how anti-semitic Jews can be.