I think it's better to avoid "deprecations by missing documentation" and document explicitly if something is deprecated.
What happens is that people working on some old code find the deprecated method, check the doc to see what it does, don't find anything, get puzzled for a while until they figure out how it works, and then use it.
If they find it and see that is deprecated they will stop using it and start using the right method.
While it's true that new users don't need to know that there's a deprecated method, it's unlikely that they will start using it, so documenting deprecated methods makes more good than harm.
If you want to remove it eventually you'll also have to go through an actual deprecation process with warnings.