Dynamically add new tags to menu?

I’m creating a WP menu that allows users to browse a blog via tags. It’s blog for a store that sells bicycle parts. So someone could use this drop-down menu to find all posts about “pedals,” say.

I’m wondering if there is a way that I could have the menu dynamically add newly created tags — to avoid having to try to set them all up ahead of time. So if the client added a post with a tag “tires,” that would automatically/dynamically be added to the menu.

It would be like a tag cloud, I guess, but using WP custom menus.

Anyone know of a plugin that does this? Or some other method?