Harry and Elaine were unknown to the White Council while they were being trained by Justin DuMorne (who was not only a member of the WC himself, but a warden). Harry didn't become known to the Council until he killed DuMorne.
We know this because Elaine disappeared after DuMorne's death and showed up later in California. The White Council tested her, but she deliberately threw the test and was not inducted. However there's no indication that they asked who had trained her (even though she clearly had been trained), or that they even cared. Elaine might not have come to their attention at all if she hadn't tried to operate openly.
So it seems clear that people of WC-level power can and do operate outside the White Council, and even do so without their knowledge.