No well, given suitable conditions, the path traced by the object in motion can still be a circle. In non-uniform acceleration, the centripetal acceleration is no longer constant and so the object's velocity is changing given that it still moves in the same circle. But yeah, it's not in the syllabus.
You may need to do some very basic analysis of the forces involved in non-uniform acceleration, and the syllabus actually makes reference to the normal and tangential components of acceleration (note that the tangential component of acceleration is the component that makes the magnitude of angular velocity vary).
See last point in the following syllabus dot point:
In particular, have a look at Q5 from the 2000 HSC, which touches on the idea of non-uniform angular velocity.