It may or may not is the question, if it was I think you would see other signs that could tell you one from the other.From the ones I have seen there carved expertly!
If you get a chance to inspect other beech trees carvings , don't hesitate.
School playgrounds and public parks in my youth had many.
Those with dates were most telling of the time it took for varied depths of cut to scar. Then expand. With some hard to tell what they started as.
Estimating age by height is an interesting contention.
Some folks insist certain trees are growing outward vs upward after a time. I'll ague trees often continue to grow upwards , at a slower rate as they age till disease or injury reduces their vigor.
And too, some species top out at average heights. Region and clime can be expected to factor.
Where limbs allow , a high carving could have been carved from a perch on a limb.
But bark healing/scarring can be more telling with study. The more by locale , the better potential for accuracy.
How old your carvings are is interesting.
How you determine age is important.
I'm not making any claims to the carvings you refer to as to their age.
Yet real old ones don't often hint of expertise after being grown over.
There are some oldies on other species too. With their creators and subjects giving clues to time of origins, (no , not treasure related unfortunately , but treasures kind of for history's sake. But of people from a known nationality and profession in a remote area.