The King-Crane Commission had no influence on the division of the Ottoman Empire, and I have absolutely no idea how you could have acquired that impression. The borders primairly reflected the Anglo-French Sykes-Picot agreement from 1916.
OOC: It's a Double-Blind What If. In the context of the thread, the King-Crane commission is to be treated as OTL. OOC meanwhile means "out of context", ergo we're breaking the fourth wall of sorts. IC meanwhile means "in context", ergo we're playing along with the idea of the thread.
IC: The alternative proposed agreement was the Sykes-Picot agreement, in which Beirut, Damascus, Aleppo, and Mosul were to go to France whereas Iraq, Palestine, and southern Syria (east of the river jordan, south of the Yarmouk River) would be British.
I don't think the Zionist Cause would have been successful without the King-Crane Commission. The British already began backtracking on the whole "Jewish Homeland" idea before it was decided that the mideast was to be governed by a series of American Mandates. Without Hashemite support via the Faisal-Weizmann agreement for a Lebanon-style autonomy within the Syrian Kingdom I doubt the Jews would have been able to resist Arab conquest.
Armenia and Kurdistan may have just ended gobbled up by their neighbors without the US mandates. Without the US troop presence, the Soviets may have pushed on Georgia and Azerbaijan. I don't think we'd have seen the series of independent states in the mideast if the British and French were administering the Arab Kingdoms as Mandates. The US was interested in setting up stable countries and then getting out ASAP as isolationism kicked in in US politics. Britain and France would have been more interested in domination of the region.
I wonder if Turkey would have been able to reacquire the international state, Dodecanese, and Cyprus if it weren't a democratic secular republic.