The UN recognition of a non-member Palestinian state status entails " a peace-loving state " and without the recognition of Israel for the Jewish people and coexisting alongside Israel, no Hamas or leader who espouses use of violence can be elected. The PA signed agreements with Israel which involve underlying mechanisms of mutual recognition. No other groups joined these agreements. Hamas cannot even be permitted to run for office if the Quartet's 3 conditions are not agreed upon.
from the article: Palestinian poll: Hamas' Haniyeh would win PA presidency over Abbas