Prior to the expulsion of the Ottoman's my understanding is that the Jews were not allowed to own land. I am happy to have this thought changed if evidence can be found to support it. The removal of the Ottomans saw the British Empire promise both the Arabs and the Jews things that if either one got given what was promised the result would be hatred from the other. This was kind of not unusual as far as the British Empire goes. In the aftermath of WW1 the British took over what is now Jordan, Israel and the Palestine territories and allowed emigration and tried to control this emigration to keep some kind of balance going on. As a result both Jewish and Arab leaders felt the other was being supported and this led to both sides forming military groups that carried out attacks that today would be called terrorism. The fact that the Jewish people got badly treated in the European countries was enough of a reason to emigrate and led directly to the US Jewish population and an increasing number of people willing to go to the middle east. The Soviet Union was no friend to the Jews present their and pogroms are hardly unusual.
No WW2 or more importantly no holocaust would not stop the desire of the Jewish people to have a home country that did not have the ability to steal all their possession's or livelihood. The only factor the holocaust created was a feeling of supporting the Jewish Homeland, some of the reasoning for this support was as much a desire to show sympathy to the plight of people whose world population dropped by so much. The fact a prominent Arab leader (mufti of Jerusalem) supported the NAZI's did not help. I still think it was possible for the Arab and Jewish people to form a country without the British Empire causing some of the problems by refusing to honour the promises made and more to the point promising the same thing to both parties.
en.wikipedia.org
en.wikipedia.org
en.wikipedia.org
the three wiki pages shown all form a part of what I have said.