Having done it that way for years, no, the name doesn't show up on mouseover–that's a SmartBookmarksBar feature. Instead of seeing the name on mouseover, you see the bookmark's “location” field, which is the actual link. And nothing when you mouseover on folders.
To be fair, the addon also has options for condensing the bookmarks bar to “squeeze” more icons onto the bar… so you can't accomplish the same look by just removing the link names. And of course there's the auto-hide option that I love but can't use because of the folders bug… ;-)