Tea brewed under different conditions will taste slightly differently. So no, on a high mountain, you cannot get absolutely the same taste as when brewing at sea level.
So no, it is not the boiling state of the water which determines the exact taste of the tea, it is the combination of all parameters, including temperature. And by the way, this is not simply a matter of altitude - if you use a different teapot or make a different amount of tea at the same altitude, you´ll also get temperature differences.
Of course, not that many people will notice the difference in taste when changing the brewing temperature slightly. And among the ones who notice, there is no telling whether they will like the 100 Celsius brewed tea more or less than the tea brewed at lower temperatures.
So, it is entirely possible to make good tea on a mountain, unless your personal definition is "there is exactly one type of good tea in the world, and it is the one brewed by my favorite process, and that process requires 100 degrees".