Not necessarily. Assad's Baathists also had a mutually beneficial relationship with the Sunni Batthists in Iraq before the war. The fact of the matter is, Alawis/Alawites are very different from Shi'a 12ers and are considered kaffir and apostates through much of the Muslim world. Not praying or fasting and celebrating Christmas will do that to do.
Personally, I think the Mullahs have decided there's no room in the Caliphate for Assad's kind, and have pretty much left him for dead. Hezbollah could have put Syria's problems to bed a long time ago if they wanted to. Instead, they've been relegated to protecting Iranian interests on the ground. I'm not seeing much in the way of votes of confience for Assad from the Iranians. But they'll howl like a stuck pig if any U.S. assets are deployed in finishing him off.
No, not that different. If Iran can openly support Sunni groups like Hamas (and the rest of the Muslim Brotherhood), they'll still accept Alawites, who themselves still are a "twelver" division. Radical Islam really laughs at the non-Muslims that think that there are significant divisions between them.
The fact of the matter is, Alawis/Alawites are very different from Shi'a 12ers and are considered kaffir and apostates through much of the Muslim world
What for? Hezbollah already has Lebanon sewn up and the Marionites acting as their willing dhimmis. No matter who rules Syria in the future, they'll remain dedicated to the Caliphate, and the current government of Iraq is on their side too.
Hezbollah could have put Syria's problems to bed a long time ago if they wanted to