Well for the most part Shi'ah only live in Syria, Lebanon, Iraq, Iran and Saudi. One of which is not Arab, however whether it be the Iranian revolution or the Shah, Iran will always seek to take power in Iraq regardless of Israel or Nasser. It only gets worse when you add the Salafi, who will not stand for such ideas as that espoused by Nasser. As well, Salafi were already causing problems within the Middle East by desecrating the tombs of the Ahl Al-Bayt. Also how will this republic fix the fact that Arabia proper would never join such a union as it goes against their right to rule and the fact that Salafi scholars had already proclaimed Nasser as Dar Al-Kufr. Also what happens if Israel is beat? Do the Arabs remain united? Maybe, but not likely.i
Well for there to be a UAR it is likely that the Islamic Revolution in Iran would be butterflied away, leaving either Shahist Iran (which downplayed religious elements and would therefore not promote pan-Shi'a sentiment as justification for a presence in Iraq; Tudeh, which would be Communist and USSR-aligned; or the People's Mujahedeen, which was vaguely Titoist with some Islamic elements.
Iraq was involved in a federation with Jordan during the Hashemite period. The Iranians didn't prevent that, so its less-likely they will be able or willing to commit enough resources to prevent a union between Iraq and the UAR.
Salafism isn't inherently destined to become a significant political and social force. There's any number of events that could cut short its proliferation.
The Free Princes movement had the potential to overthrow the Wahhabi monarchy in Saudi Arabia, and I have a tendency to think that without Saudi Arabia to form the keystone of the Arabian Peninsula, most of the countries there would be relatively easily-coerced into joining.