Mpix uses Kodak E paper among others, the back reads "Kodak Professional Endura Paper" but doesn't specifically have any copyright notice on it.
You actually do have a time limit to register the copyright. It has to do with the first use of the image rather than the date it was taken I believe, something like 90 days. Plenty of reading on the Library of Congress website. There are books out there to help make sense of all of this. But honestly, I don't go thru with it. I know a lot of people who don't - but if there's a need, once it becomes part of a workflow you might as well...
My cynical reasoning (with good reason but that's another story) is that anyone with a flatbed will just make their own prints anyway whether they know or care about copyright, and if the quality isn't as good these people don't seem to notice or care.
So I don't worry about what I can't control and charge a decent amount for the first print, and make it the highest quality I can. YMMV - don't sweat the small stuff!