If you did, you could DMCA claim it. They'd still archive the stuff, but it wouldn't be publicly available until whenever it'd fall into the public domain. That part of the system seems to work fairly well, except the century it would take for it to fall into public domain.
You probably don't even need to make a DMCA claim. Probably just ask them to take it down. That's pretty much how the IA has operated in general. Mostly just act as if most people don't care (which they don't) and, for most other cases, take any requested actions because it's easier for both sides than a lawsuit.
The important part of the DMCA claim is that you state under threat of perjury that you either own the copyright or are a representative of whomever owns the copyright. That's why they'd probably want a DMCA claim or some other verification you owned the copyright on what you want taken down.
If you did, you could DMCA claim it. They'd still archive the stuff, but it wouldn't be publicly available until whenever it'd fall into the public domain. That part of the system seems to work fairly well, except the century it would take for it to fall into public domain.