There'd be Jews there from earlier migrations through the 16th-19th century. But their population wouldn't be so hard to be an issue and Zionism wouldn't be as mainstream as it is post-Holocaust.

I'd imagine most Jews would be trying to live as they can in the new states of Syria and Jordan post-Ottomans, sharing in the same trial and tribulations as their Assyrian and Palestinian neighbors. Unless it's encourages externally later on, or the years in PoW drag on and there's discontent with Jordan or Syria for one reason or another than I could see Zionism taking on, if in a different context and situation to break from their Arab masters.

But since Jews are people of the book, I can't see it being much a thing unless Islam somehow radicalizes, which'd mean some manner of interference from outside all the same I think.