WA is an "At-Will" employment state.
That means a worker can be fired, for any reason at all, or no reason at all. Poof, your job is gone. http://www.rbs2.com/atwill.htm
Can he carry? Sure, but he'd be breaking company policy and would likely lose his job if caught.
Would it be a criminal offense? No likely, unless he (as a part of his job) carried on school owned property or federal property.
Can he fight the policy? Sure, he can talk to his superiors and try to get an permission to carry or get the policy changed -- but it will go no where and it will jeopardize his job and future promotions imho
As someone else stated, it all sounds contractual. He accepted the job, and accepted the 'terms of employment.'