Oh yes, I made that mistake when we went to Yosemite and went up Glacier Point 7,000 ft they day after getting there. I got so sick it was hard just driving back down the mountain.
The highest point in the Smokies is Clingman's dome, almost the same elivation but have never experienced the same problem there as I did in Yosemite.
Maybe altitude sickness is like getting sea sick? I used go on dive boats all the time and laugh at the guys hanging off the back of the boat throwing up, then one time it happened to me too.
Edit to add: Field Service Sucks! (Just to stay on topic, I would rather get altitude sickness before going out in field service.)