Hi,
It's an interesting question, mainly because it's tricky to answer...
The currency switcher is currently a Joomla module, requiring to be placed at some template position. Now, please keep in mind that in Joomla any menu also requires to be placed at some template position. So, if you're quasi suggesting the currency switcher to be somehow available as a Joomla menu item (however that could be realized, if at all), it would either need to be placed as a separate menu in a template position (same thing as with the module as it still requires a space), or be added to a menu that already exists in your site.
The latter is already possible, eventually: Many menus, e.g. the ones often referred to as "mega menu", allow you to place a Joomla module inside, so a module would appear in a dropdown, and that would probably solve your case.
It depends what you are using on your site, what eventually already came with your template. So, check your present menu(s) if they allow such functionality. Eventually, simply try publishing the currency switcher module to the same position as your (main) menu and see what happens in the frontend.
Hope it helps. Otherwise, if I got completely wrong what you meant, please explain what you want in a more detailed way, perhaps by adding a screenshot mock-up.
Edit:
Sorry, initially I've been using the term "language switcher" all the time... probably because I've just been dealing with the language thingy in a project...