Only if one considers a work that lacks a copyright header something that is in the public domain, which I belive is not the case.
Well, certainly work that is PD would not have a copyright header, because it wouldn't be in the public domain if it was copyrighted. However, a copyrighted work doesn't have to have a copyright header.
I thought that PD works must have a header that notes that it is in the public domain. Which is more or less a copyright header, since PD still falls under the laws of copyright law. But oh well..
Cheers.