Yeah, more likely you'd get a Cease-and-Desist. But once the ArchiveTeam publishes it, they'll likely get DMCA'd (though they've survived things like that before).
Not to mention that dying websites or recent acquires are likely to be able to have the legal muster to start threatening archivists.
https://en.wikipedia.org/wiki/Online_Copyright_Infringement_...
This is not to say that people don't send "DMCA notices" for anything and everything to anyone and everyone, but those notices are not following the law. (Also, a lawyer can always send a demand letter demanding that someone stop any behavior, but a properly-constructed DMCA notice gives the recipient an extra reason to follow it compared to a run-of-the-mill legal demand—"[a]n OSP who complies with the requirements for a given safe harbor is not liable for money damages", as Wikipedia puts it.)