If you geotag a place that is easy to get to, you may have a detrimental influence. However, if you geotag a place that takes a long hike to get to, especially off-trail, multiday, and uphill, you are likely to have only a zero to very small impact.
I base this conclusion on our experiences in the California Sierra -- even Yosemite -- and the Colorado Rockies, where we could go days without seeing anybody, even in the distance, if we were off-trail and a thousand or more feet above the trailhead. Even more modest hikes attract few people beyond an obstacle that looks difficult (but is not).
A comment from a local quoted in the chapter The Moab Treehouse in Escape Routes by David Roberts is pertinent:
The legacy of secret-keeping is what gave us Glen Canyon Dam. "The Place No One Knew."
Glen Canyon was a magnificent complex of branching canyons in Utah and Arizona. It was little known -- not remotely as famous as the Grand Canyon, hence the title of the book The Place No One Knew by Eliot Porter. The Grand Canyon was saved from being inundated by a dam. because of widespread public outrage, but Glen Canyon, known only to a very few, was not. Boating on Lake Powell throughnear the partiallytops of the largely submerged canyons is, for many, a poor tradeoff. Edward Abbey wrote a novel The Monkey Wrench Gang, whose target was a thinly disguised Glen Canyon Dam.