if a runner were suddenly competing at a higher altitude than the one the runner had been training at, then the performance would be lower. See the attached article on high altitude and athletic performance which will make this quite clear http://www.rice.edu/~jenky/sports/altitude.html.
That runner would definitely be struggling more in the higher altitude, where there’s less oxygen available compared to lower altitudes. Training adaptations are very specific – it’s no secret why our U.S. Olympic Training Center is located in Colorado. Training at high altitudes pretty much prepares you for the worst conditions you might have to compete in.
You should look into proper training progressions for adjusting to higher altitudes. There are a number of variables to manipulate. Everyone will be dealing with the same conditions, but with altitude the more time spent in that environment the more adapted the body will be. I used to live in Colorado and I loved coming back to Hawaii for visits and just smoking on the bike and in the ocean. But after about 10 days I could tell that I had really lost most of the advantage of training at altitude had given me.
I don’t know what altitude you will be competing at so I will assume 8000 feet as an example. If possible I would train (or train my athlete) at 4000 ft. for a few days and try to have our lodging at about 6000 ft. Then I would move us up to train at 6000 ft. for a few days and move the lodging up to 8000 ft. I would then train at 7000 ft. for a few days and then at 8000 ft for a few days and move our lodging up to 9000 feet. I would stay up at the 9000 ft for as long as I could at that point and train up there as much as tolerated. The tolerance is the important part. If I or the athlete experienced altitude sickness symptoms, I would be wise to revise the process. This is of course just a theoretical model.
I can also tell you that if the athlete is not accustom to altitude, trying to compete at an event at over 5000 ft will be very difficult. And for every 500 ft of altitude over that it gets quite a bit more likely that a person will experience issues. At 8000 ft the chance of getting into altitude sickness is very likely. I can’t remember everything on this, but I do know that it affects the fluids in the lungs and even the brain. And people die from this when it is totally avoidable. You should really look into this well before you get to your event.
Not knowing what altitude you intend to compete at, I have gone with the scary version. I would rather find out that I had no reason to be concerned than not at least give you a warning. Good luck.