This contradicts everything I was ever taught by Claudia Rapp (Now Professor of Byzantine History at Vienna) and Barisa Krekic (Emeritus, UCLA). Given the approaching lectures in the Byzantine Course I am teaching, I will be in a better position to bring specific sources and scholarship to bear shortly.
I look forward to it. For context, I did my undergrad dissertation on the sixth century Egyptian Dioskoros of Aphrodito, so read quite a lot about the context. Mark Whittow puts the best argument on the matter, but there are others around that are in broad agreement with his basic point that the supposed alienation of the anti-Chalcedonians is enormously overrated as a factor in the Arab conquests.
I recall all of this and agree that it would have been difficult to take Constantinople in 626, but it would not have been impossible. Yes, easier for the defenders I grant you, but this is an alternate history site and the less though still possible may be entertained without it being instantly refuted as highly improbable. I was always taught that the siege of 626 was a severe danger to the Empire and have seen nothing since to make me change that view.
Oh, sure, we can entertain the possibility: and I wouldn't suggest that Constantinople falling at any point is impossible. But if you put the POD on, say, January 1st 626, then the chances of the siege succeeding really are tiny for all the reasons set out in this siege.
Now, if you constructed a scenario where, say, the Avars develop serious naval power in the 610s, and the Sasanians concentrate on thoroughly subduing Anatolia rather than just raiding, and Egypt and Syria and Africa are somehow detached from Constantinople by, say, a pretender, then the City falling becomes a possibility. Still a very slim one though, IMO.