For the boss to want to take such a strong stance on this, it seems to me that this has been a big issue for your company. I think the better solution then putting together a policy is to find out why. If you are finding a number of your employees' resumes online, then you need to find out why these individuals want to leave. Is it the environment (culture), job duties, pay, hours, benefits, etc?
If I find an employee's resume online, I will sit down with them or have the manager sit down with them. Sometimes we can save the person and fix the issue and sometimes you don't want to save the person (if they have bad performance, attitude, etc.)