Yes, but that intuition doesn't seem to work for the case where small disk is rolling around the inside of large one, not outside. What's the intuition for why we then subtract one rotation rather than adding one ?!
In the original SAT question, the center of the rolling circle is 4r from the center. That means it travels an arc of 8pi. Then assuming no-slip, that works out to 4 rotation.
In your case, rolling on the inside, the center of the rolling circle will only be 2r from the center. Using the same logic, this yields 2 rotations.