They can exist surely but not on the Israel's expense like they tend to. They have no authority of any part of Jerusalem,hence they have no right to claim the holding of presidential elections in East Jerusalem . on the same principle I will ask ,if the Israelis could demand to vote In Gaza ,in Egypt or in any other country? Well the answer is clearly obvious.
Pakistan air strikes against Taliban kill at least 25 (Reuters)
from the article: Hamas demands Palestinian elections be held in East Jerusalem