hmmm I figured this post would be about the opposite problem -- when people use WP Login methods to put a password on their front page, yet their feeds are still wide open to public viewing & Google cache.
If you use the cpanel password method, I don't know if it is possible to let your feeds out. In any case I think the feeds would either be totally public, or totally inaccessible... I've not yet seen feeds that are shown Only to password-aware subscribers.
If the feeds were totally public, you could probably avoid having random readers because they'd never get into your site to notice the feed link... but you should be aware that Google or a bot might find your feed address and cache it or link it somewhere beyond your control.