I've just played a couple of holes in the Unity game, one as a ranked round and one as a practise round.
In the ranked round I putted up close to the hole and got a 'performing-auto-click' to finish out the hole. Checking out the ball degradation value after that, showed that the ball registered no extra hits after getting onto the green.
In the practise round, again I putted up close to the hole, and then took the 'gimmie'. Checking the ball degradation, this again showed that no hits were registered after I reached the green.
The image below shows the degradation on a new ball after the two holes I played. Two drives and two approach shots equal total degradation of 4 shots including all putts, auto-click putts and gimmies.
Hope that helps.