A huge issue with this is that the Islamic Republic in Iran has, however arguably, a precedent. The veliyat-i fatiqah that the ayatollahs rule through is technically existent because the 12th Imam of the Shi'a, the Mahdi, is not on Earth to guide the faithful.
As black angel stated, most Muslims are Sunni, and since, under Sunni ideals, the khalifa doesn't need to be of Ali's bloodline, it could be anyone. The idea of an Islamic republic doesn't make since, but a restored "caliphate" could be interesting.
However, it could be possible to see these things pop up (however unlikely) in Iraq, Bahrain, or Azerbaijan, all countries with high Shi'a populations that have a precedent in the post-Revolution years for movement towards such a state.