Legal Question in Employment Law in Illinois

Yes, depending on various other circumstances. Assuming this is a job "at will" (most jobs are in Illinois - you can quit or be fired any time for any or no reason) signing the policy as a condition of keeping the job may be valid if all employees in similar positions have to. If there are additional factors you are not stating, or there is something like a work contract that does not obligate you to sign off, the answer could change....