Wrong. As you can see at The Doctor (The Brain of Morbius), several accounts of pre-Hartnell Doctors show the Second Doctor (or beyond!) as knowing perfectly well that these regenerations existed, so it doesn't fit into the Timeless Child framework. As with turtles — it's alternative accounts all the way down, my friend.
(And please avoid the term "canon". The Brain of Morbius was always valid, and beyond that simple fact, we do not concern ourselves with building a self-consistent "canon".)