The Reish Galuta, or Exilarch, was, from the time of Zerubavel until the abolition of the office ca. 1000 C.E. (with interregna), a Jewish political leader descended from malchut beit David. In some ways (see the Wikipedia article) he was treated as a legitimate king and heir to the Davidic line.
Was it assumed that the then-current Reish Galuta would reign as Melech haMoshiach if we were to have merited Melech haMoshiach's reign?