They would have their hands full settling the situation in the Middle East to bother with much in Europe; also if they are interested in maintaining the forced export of Jews, who would be reinforcements/additional help building up Israel, they would have to stay on Hitler's good side. Of course once Hitler conquers Poland that would mean Israel has to be willing to accept some 3 million people in a matter of a few years; France/Belgium/Holland/Norway/Denmark adds in hundreds of thousands more, while Barbarossa would add in millions.
Prior to 1939 there would only be some 100,000 or so Jews in Germany and Austria that needed to get out, but couldn't (IIRC something like 300k got their 'Aryan' status by special appeal), so these could be handled in this smaller version of Israel IMHO without too much trouble. Until 1942-43 I don't think the Hungarian, Italian, Slovak, or Romanian Jews were targeted by the Nazis, so wouldn't need a home until then.
But this Israel, not to mention OTL Israel, would not be able to accept the millions of Polish Jews, so that would be a serious issues, especially if (when) the partition causes massive violence in the area. If anything it would end up tying down more British resources to establish an Israel than put off the situation. The Israelis can offer to take over more duties from British forces in the area, but I doubt they would be accepted, considering what it would mean from the Arabs in the region.
Not only that, but when there is violence in the wake of the partition, Israel would be too bogged down defending its territory or trying to take more to make more room for Jewish refugees to participate in the war in Europe. Plus to avoid pissing Hitler off and having him take it out on European Jews, I doubt they would want to get involved other than to offer to take on Jewish refugees if Hitler would let them go peaceably...not sure how peaceably that would happen though.
I thought Lehi tried in 1934 and then was too angry at the Nazis for their treatment of Jews to get much further than that. Also IIRC Hitler wanted to court Britain at the time, so didn't want to antagonize her by supporting a Jewish revolt.
That would put them at odds with the British at an awkward time, which would effectively make them allies of Germany and would let the British align with Arab interests, something Israel really wants to avoid. I think neutrality while getting Jews out of Europe and building up for a post-war show down for the expansion of Israel would make much more sense realistically. There would be enough fighting as it was in the Middle East as a result of Israel being created to keep Israel occupied before 1940.