It should not have been a surprise to UNESCO when the US pulled its funding, which accounts for 22% of the agencies’ budget, following the acceptance of Palestine as a full member. In US law it is written that the US will withdraw all funding from any UN agency that admits Palestine as a full member prior to a peace deal between Israel and Palestine. The moment Palestine signaled its intention to join UNESCO, the conversation should have occurred about how to make up the inevitable funding shortfall that would result.
Circumventing the Israeli/Palestinian peace process may be a necessary step for Palestine in order to pressure Israel into concessions, but this approach does carry some short-term consequences. The first consequence, as is mentioned above, is financial. Any UN agency that accepts Palestine as a full member will have its US and Israeli funding cut. I am not sure how much US contributes, but I imagine it is a significant amount. This loss of funding could severely impair an agency’s ability to operate effectively.
Outside of funding, the Palestinian government may find that recognized statehood, outside of a peace deal, may not serve to advance their interests as much as they wish. It may not become just an arena from with to rally support to pressure Israel. This tactic may prove to backfire a bit as pressure to shore up the unprovoked rocket attacks by Hamas militants may be a type of unwanted attention statehood brings.
Israel, with its unique history, geography, and national thought, will most likely continue to operate just as it has, regardless of whether Palestine gains full UN statehood or not. The US will not abandon Israel anytime soon, barring a major geopolitical faux pas like the use of a nuclear weapon as a first strike, but even the absence of the US will have little effect on the direction of Israel’s foreign policy. They plan and execute their foreign policy with the expectation that they are on their own.
So Palestinian statehood, absent a peace deal with Israel, really only hurts the UN budgets and draws more pressure on Palestine. If the UN accepts Palestine with full statehoods, will the US withdraw all of its funding to the UN? Unless the law is changed, that may be the case. Will increased pressure from the UN bend Israel into giving more concessions in the peace process, probably not, but I guess its Palestine’s only option these days. Bringing an end to the conflict between these two groups requires tough measures and new approaches; maybe this will start the process in a different and more productive direction. I'm guessing that this will yield more chasing each other around in a circle, going nowhere and gaining nothing.