Given your stated reason for the policy, I would not take it seriously at all; whether I followed it would be purely a function of how much I wanted to humor you or were afraid for my job.
If you want people to follow it, reconsider the motivations and have a reason they can take seriously! And if you can't, you might find another way to achieve the effect you want, such as not putting monitors in places where visitors can see what's on the screens. (that's probably a good idea anyways)
Just to be clear, I'm not trying to mock your situation; you may, in fact, have a very real problem that you're trying to solve.
But the important thing to how your employees behave is not the reality of the situation, but how they perceive the situation. The way its presented sounds like a knee-jerk reaction that might not even solve the problem that might not even exist.
And furthermore, you may not think you're asking much of them but little interruptions can be a serious disruption to a person's workflow, so they have real reasons not to just go along with things.
Thus, the need to reevaluate the motivations; to let your employees see that there is a real problem, this policy will actually fix it, and there isn't a better alternative that doesn't disrupt them as much, assuming these are all actually true.