I tried that — but all that happens is that the icon is removed; instead I get a question mark in the Finder toolbar.
BTW, I noticed that after clearing the checkbox next to the Dropbox extension in System Preferences, it automatically is checked again within seconds. It looks like there is some Dropbox process running in the background that does that.
Interesting you're not seeing it anymore; I can't get it to stop and it appears to the very left, always in my way when I want to backtrack. I'm at the point of getting rid of Dropbox altogether and forgo the convenience of syncing my iOS and OS X apps at this point. I can't believe the Dropbox team is doing this.