From what I understand the bulk of Spanish Jewish refugees escaped to North Africa, particularly Morocco, while others would settle across the North African coast and eventually establish major communities in Salonika and Constantinople. While the migration northward was smaller, other Sephardim established important communities in Genoa, Venice, Bordeaux, the young Dutch Republic, and even as far north as Hamburg and Altona.
Were Sephardi Jews in Danish Altona aware of their distant relatives living in Morocco, essentially the other side of the known world? What kind of contact, direct or indirect, existed between Sephardi Jews in Christian Europe with Sephardi Jews in the Islamic Mediterranean?
So while I don't know the answer to all of this question, I do know that after the expulsion of jews from Spain an effort was made to resettle at least some of them in the Italian town of Livorno. Presumably, yes - the idea was that their far-flung connections would aid the town's economy and turn it into a more prosperous mercantile hub.
In the specific case of Livorno, Tuscany's ruling Medici dynasty had long favored its harbor in a conscious effort to limit the influence of nearby Pisa, their duchy's second-most influential city which unfortunately had the annoying habit of periodically revolting against their rule. Inviting jews expelled from Spain was one of many things done to foster the harbor's growth. You can read the longer story in this answer, and this other answer which I guess the reader didn't like given their downvotes.