I am a law school graduate. What I offer is mere information, not to be construed as forming an attorney client relationship.
The problem here is 4th Amendment right against illegal search and seizure is only found against government (i.e police). It doesn't apply to private individuals. What does apply to private individuals are the notions of trespass and conversion of property, which seems the employer is trying to supercede by asking for your permission.
This is quite unreasonable.
Check your state law about this by looking at the labor code or employer-employee code. Go to the state laws section at the freeadvice.com homepage and click on it, then click on state statutes. Then click on your state and go from there.