Zionism was especially based out of the USA, so it probably depends on whether the Ottoman Empire feels any need to placate American Zionist organisations. If the USA helps the survival of the Ottoman state, either through diplomatic actions or loans (I assume a Muslim state could accept loans?) then the Ottomans may be open to persuasion to greater immigration, because they can't read a history that has not happened yet and won't know where it might lead.
If not, then Zionism probably remains a largely American/high-brow thing and ordinary Jews would show no great inclination to try to move en masse to Palestine, especially since without financial backing the land they can buy up is the worst kind and the hardest to make a living on.
Without the Zionist focus on Palestine=Israel as a homeland, there is no real need for Jews as a people to migrate anywhere. In most of Western and Central Europe they are assimilated and successful populations, further East it depends but the pogroms in Imperial Russia were not because the Jews were seen as poor and downtrodden. Ottoman survival presumably means a Central Powers victory so we probably get an independent rump Poland, and some German influence in Russia, so there won't be mass expulsions and refugees fleeing for their lives.