Alternatively, what if the Shia ended up in Iberia instead of Mesopotamia and Persia? The pressure from Sunni North Africa might be enough when coupled with the pressure from the Christian kingdoms to force a Shia al-Andalus to stay united.
Impossible. The first Imam had fled to Karbala because he wanted to get safety there. It was before they even had Spain.
The Shia didn't have Iberia as one of their Da'was(It's a missionary 'region', literally 'call'). They focused on Persia because of its large population of Shia and because the Buyids, who controlled Mesopotamia and most of western Persia were also Shia. The Shia wouldn't be interested in spreading there, not to mention that there aren't any supporters for it in Iberia. When the Zirids broke off as a sunni dynasty from the Fatimids, you lost your chance for even missionary work.