Absolutely ... I've had a punctured ear drum in my right ear since I was born ... didn't keep me out of the service, though ...
Funny story: during the US Army physical they gave a hearing test in a booth with headphones ... I guess some guys would deliberately try to fail, because right after the hearing test was a color blindness test ... the guy at the desk would be looking down and tell you to read the numbers you see on the multi-colored pages ... if you started to read the numbers, he would mark "Hearing, Good" ...

But as Bill said, the hearing test has to be given under very controlled conditions ... When you are in the booth, you don't hear anything other than what comes through the headphones ...