Is the dispersal of the Jewish people to all parts of the globe a necessary precondition for the Redemption?

Ever since creation, sparks of holiness have been scattered throughout the world, awaiting their redemption when a Jew comes along and performs a mitzvah in that location. When someone dons tefillin made from the skin of a local animal, or makes a blessing over the water from a nearby pond, the sparks of holiness in that place are elevated.  In other words, every mitzvah that we do draws in the sparks of holiness and returns them to their heavenly source.

The "redemption" of all these sparks is indeed a necessary condition for the ultimate Redemption to come. As long as there remain sparks to be refined; as long as there is a place in the world where a Jew has never lived or fulfilled a mitzvah, that area is still in exile. This is one interpretation of the saying of our sages, “The Jews were not exiled among the nations, except so that converts should be added to them” (Pesachim 87b). These "converts" refer to sparks of holiness that are like strangers in a strange land, awaiting their redemption by the mitzvot that a Jew fulfills.

 It is apparent, then, that if a Jew does not reach a particular location in the world, that area remains in exile and the full Redemption will be delayed.

 However, Chassidic teachings explain that these sparks can be redeemed even without a Jew going into exile. The spiritual process can be carried out even if the Jewish people would have remained in their own land and fulfilled mitzvot in an exceptional manner, in both quantity and quality. Then the mitzvot would have served as a spiritual "bonfire," joining the sparks together of their own accord.

 Thus, exile is not a necessary component of the redemption process. Being that we did not merit the redemption in this manner, it remained to us to be personally exiled and redeem the sparks one by one.

The process of "refining the sparks" has already been completed, as the Rebbe has informed us. We are ready for Redemption at any moment.

Sources: Torah Or, Bereishis 5:4. Likutei Torah, Bamidbar 3:4. Likutei Sichos vol. 30, p. 252. Toras Menachem 5752, vol. 1, p. 401