I saw more than one trainee/airman who decided to not disclose they had asthma and their condition reared it's ugly head at the worst time for them. One kid had an attack during a commanders PT run. They sent him to the hospital, he played stupid and he was gone like yesterdays trash. Another had an attack right after a ruck march, the docs figured it out, she copped to not disclosing her condition at MEPS and they sent her packing with a fraudulent enlistment.
I saw other people who ended up being diagnosed with exercise induced asthma after they'd been in awhile, but they went through hell with their PT scores and leadership until a doctor would diagnose them right. However their military careerers were done after that. I've spoken to tons of people who think the military's stance on asthma is wrong who wanted to join up, but I can tell you the military just isn't the place for that kind of problem.