If you are not forthcoming about your injury, you can be terminated. They don't tolerate lying, which is what you would be doing if you withhold information. For example, one recruit pulled out her inhaler during a run. She got fired since she "forgot" to mention asthma in her medical Hx.
Speaking of runs, you'll be doing a lot of running, even in the "crossfit" style academies. When you eventually drop out of a run, or favor your injury in some fashion, you'll be pulled for "fit for duty." You'll be sent for a medical evaluation, where they'll then discover your condition. They'll want to know why you didn't mention your condition before starting the academy.
You can be dismissed from runs and be placed into alternative forms of PT until you heal. For example, I had knee bursitis. I was excused from runs (this was before suppression training) until I healed up, but the trainer worked me in other ways while the group ran.
