Is it possible to create an invisible rule in Mail? I'd like to apply a mail filtering rule within Mail without it appearing in the rules list. Is there any way to make this happen, either from within, or from outside the app?
No you cannot do that within Mail.app.

However you can add for example a mail filtering proxy that sits between your mail provider and Mail.app. This proxy will be able to filter away mail without Mail.app displaying that it does so. Depending on your mail provider it might also be able to move mail into subfolders, etc. (for example this is possible on IMAP).