No, under a proper understanding of American law:
A government may choose to ignore certain past arrests for its own purposes. It may choose not to disclose such arrests to others. It may even authorize people to lie under oath about those arrests (I set aside in this post the question whether that is a sound idea). But the First Amendment protects other people’s rights to talk about arrests that had — as a matter of historical fact — actually happened. A statute can’t rewrite history, and force others to pretend that something didn’t happen when in fact it did happen.
Via Volokh Conspiracy.