the documentation for shinydashboard doesnt seem to support this in a straightforward manner.
However there is a dropdownMenuOutput() you could place in your ui, whose sole param is the outputId. (therefore you would have an id of sorts for it).
The complication is that you would have to stipulate its contents by providing a renderMenu() in the server code for it like
output$id_of_my_menu <-renderMenu({
#the UI things it should contain
})