I can't imagine they would, as it seems it would be difficult to identify clenbuterol, distinct from albuterol. And with the insanely taxing rigors of boot camp, relative to the high prevalence of asthma among the general population, I'm sure there are hundreds of thousands of serviceman who use their albuterol inhaler regularly.
If you want further peace of mind, here's are two good resources to read over:
DOD (Military) Urinalysis (Drug Test) Program
Military PlainFacts » Seven Secrets of Military Drug Testing
EDIT: Suspicion confirmed. The IOC tests all Olympic athletes for clenbuterol, and albuterol does produce a false positive. Curious, because a regular 12 panel drug test can easily isolate hydrocodone from oxycodone from morphine. I don't know why the same level of sophistication doesn't exist when testing for beta 2 agonists, but that's because I don't know much at all about the science of drug testing. To reiterate for clarity, though, the military does not test for clenbuterol.