I, too, live at altitude (in Colorado 7,200 ft) and train often between 6,500 - 14,000 ft amsl. In addition, since
@jsalt mentioned it, I have climbed/summited Kilimanjaro. Before moving to Colorado four years ago, I lived most of my life in the 800-4,000 ft range. Living/training at altitude, I can tell a positive difference in performance not only at higher altitude, but also at lower altitude. Further, at sea level it feels like I am "supercharged."
Google the term "benefits of training at high altitude." There are countless articles and web sites that explain the benefits of live high/train high and athletic performance at lower altitudes. The body adapts (acclimatizes). Specifically, the hormone EPO triggers red blood cell production to help get oxygen to the body. Many athletes refer to it as "legal doping."
Since you live in the Andes, it's seems safe to assume, in addition to altitude, your training regimen includes access to many hills. As others have stated, if you train at/above 8,300 ft with the gear and pack weight that you will be using on the Camino, you will most likely have a very pleasant go of it physically.
Buen Camino!