If someone has a prescription for a controlled substance and stores it in their desk at work, can they get in trouble? Can someone get in trouble if it is discovered?
In general property owners and employers can impose any rules on their property and employees (respectively) that are not prohibited by law.
Granted, there are extensive statutes and regulations to protect "employee rights." I have not heard of protections that include "possession of prescribed medications," but that does not mean they don't exist in your jurisdiction.
If you really want to know whether you have a legal right as an employee, and you can't find it in written law or regulation, you would have to consult regulators or employment law attorneys in your jurisdiction. (As a practical matter, of course, it might make sense to first find out whether one's employer wants to assert a policy infringing the right in question.)