If only Germany would not be willing to recognice Palestine, then this might happen, but that is not the case. France and Italy the two next most powerfull countries do not recognice Palestine either.
Germany is usually fairly happy with the current state of the EU. The things Germany wants to change are usually also supported by Spain and that means blackmail is harder. The only exaption to that is finance. However Spain is not going to let billions go to waste to have Palestine recogniced. That is just more of a symbol, rather then massivly important.
Also Germany leaving the EU would cause some massive problems in other EU countries as well. They would hardly be cheering for it.