It changes state on the server, i.e. the counter. So no.

I’d say it depends on what the counter is for. If it’s used to bill the user per pageview, then it’s user-visibly not an idempotent action, so no. If it’s used to estimate site speed, then the user doesn’t care, so yes. (In fact, analytics is the example I see most often under “non-idempotent stuff it’s OK to do on a GET”.) If it’s used to display a counter in the site footer, then you might wish the user cared for your bragging, but they probably don’t, so yes with a disapproving glance in your general direction.