User-provided content is provided under a license between the user providing it and the site hosting it -- inherently, because otherwise the site wouldn't be allowed to do anything with it at all. Generally this takes the form of the site's ToS saying that the user gives the site a perpetual license to use the content however they want, but generally not an exclusive license.

As such, and I'm not a lawyer and can't promise this is true, I suspect that reddit couldn't actually do takedowns on someone who's archiving their user-provided content. Any specific user whose content was archived without their consent could do so, however.

When Reddit owns the delete button, they control what happens when you press it. There’s no need for them to rebuild their deleted history. It’s still there (even if it’s inaccessible to the world)