My being able to get used to living at 4500 ft and hiking up to 6000 ft, after living most of my life at sea level or lower is a great testimony of the adaptability of the human body...
Heck yeah. We went walking on the hills in Los Maples once and I was sucking in O's.
Most of my family has found that it takes about 3 weeks for the dry nose and nose bleeds to subside after moving from sea level to 4500 ft. Once your nose is acclimated, it is much more pleasant. Physical exercise in the thinner air is also a bit more challenging. I spend time on the tread mill and lifting weights so that my trips to Yellowstone are a breeze. That bumps the elevation to the 6200 to 8500 foot range. Absent sufficient preparation, a visit can be fraught with lots of huffing and puffing up the trails.