If the Shia end up being a pillar of Roman control in mesopotamia will they ever be considered a Noble Herasy? It might be a pretty hard pill for the romans to swallow but making them a ruling class and not persecuting them might help them become a loyal minority along with the kurds
They might end up being the preferred sect of Islam to Rome, but they remain exactly that - Muslims in the eye of a solidly Christian state, extensively theocratic even by the standards of the time. Given that the Romans can't stomach the notion of extending clemency to the Nestorians, I can't see them doing so for an entirely separate Abrahamic religion.
We can't forget that there is an old (if now small) history ITTL of Anatolian Sunni Muslims who have been relatively well treated (he says, dreading the though he has forgotten something). Realistically I think the Shia would be in contention with that group, but keep the two seperated, and I can see the argument for it.
Raised to Noble Heresy status though? Impossible. The only way that could happen would be to stop being Shia Islam and effectively become a form of Christianity by acknowledging Jesus as the Son of God and divine. THAT would be an incredibly useful heresy for the Romans if the Time of Troubles and the recent banishments and enslavements in Syria hadn't happened. (And that still doesn't account for the headache that would be melding the Trinity with Muslim views on Jesus).
I'd say the Shia community has a more valuable use to the Romans than being local rulers though - and that is being a form of anti-Ottoman force, behaving like the Ismaili Shia.
However that is still unlikely, as really - in this timeline, working the Romans as any sort of Muslim power isn't exactly going to make you popular with the rest of the Muslim world. Georgia? Maybe, but all of it is pushing it.
I think the best relationship would probably be tolerance from the Romans, with the Shia essentially using the Romans as a shelter to operate from. That might mean working to keep the peace on the Romans behalf, but also that there isn't actually loyalty, just mutual self-interest. The second there is a large Shia power that can realistically take over where they live, I'd expect a flip.