As far I'm not familiar with GIS, my question can sound strange 🙂
Is it possible to calculate longest (theoretical) line of sight (in Earth)?
I found many tools which can calculate line of sight, but you must know at least point A, which in my case is unknown.
You could use a DTM of the world and invert the heights (calculate max height - height) and use Sink—Help | ArcGIS Desktop to determine the sink locations (these will be the peaks). With those locations start the process of evaluating the lines of sight and see which one is the longest. This will take a considerable amount of processing capacity, but is feasible.
BTW, I just stumbled upon this list of The Ultra-Prominences Page that contains a KMZ you can download and use as your locations. This is a list of "ultra prominence" peaks and could be a good start (based on SRTM):
Prominence is the relative elevation of a mountain summit. Prominence is the elevation difference between a summit and the highest point (saddle) that separates that summit from any higher summit.
You also have to remember that the highest locations need to be surrounded by low elevations in order to see past them. So even if you were standing on top of the tallest mountain on earth, surrounding mountains, or even plateaus would obscure the ability to see a parcel of land further on.