Depends what you consider canon. Before the New 52, the Kingdom Come universe interacted with the main DC universe, and there was a Batwoman in that. There was also a Batwoman in the Superman/Batman comic that interacted with the main DCU, as well as a Batwoman in the Titans of Tomorrow universe in Teen Titans and they interacted with the main DCU on more than one occasion (even post-Rebirth). Being in a multiverse reality doesn't mean it's non-canon.
That analogy doesn't work since Kate Kane isn't the first Batwoman. In that case Kate would be Patience in that scenario.