I'd agree with this: the same goes for the supposed letters to Heraclius.
As for Byzantium in this scenario, I'll make the point that I always make, and is always ignored: namely that a "Coptic revolt" is extremely unlikely to happen. There wasn't a distinct Egyptian identity to forge such a revolt in the seventh century. All of the educated classes who could have led a rebellion were thoroughly culturally Greek (which of course in the East is synonymous with Roman) and part of a world that clearly looked towards Constantinople and the Mediterranean, rather than inwards to Egypt. Furthermore, the total absence of religious revolt against Constantinople by anti-Chalcedonian provincials in either period of Roman/Byzantine rule over them (fifth to seventh centuries and tenth to eleventh centuries) is I think suggestive.
About the only chance I can see for a breakaway Egyptian state is one happening almost "accidentally", with a rebellious general somehow taking Egypt but being unable to advance further from there, and Constantinople being unable to deal with the pretender. The Egyptian army itself was pretty marginal compared to the major forces stationed on the Danube and Euphrates, so I think such a rebellion would have to initially begin outside Egypt, but end up being contained to there.
In a scenario where the Arab (I deliberately don't say "Islamic", because I think it's dubious as to whether the first generation conquerors were actually Muslims as we understand the term) conquests are aborted early, the slow reconstruction of Constantinopolitan rule over the Eastern provinces continues. An early priority will be to put together some sort of doctrinal fudge that accommodates non-Chalcedonian opinion, and, assuming no further military disasters, there's no reason this shouldn't stick. Monothelitism IOTL after all was abandoned after continued Arab successes in the 670s made it abundantly clear in Constantinople that God's favour had not returned to the Empire: the same goes for Iconoclasm in the 830s. Unlike Iconoclasm, a Chalcedonian fudge doctrine is unlikely to incur significant popular disapproval, simply because most people won't understand it: so I think it has a significantly greater chance of sticking.
In military terms, it all depends on how quickly Iran is put back together. Assuming a relative respite in the East that lasts for, say, a generation or so, I'd imagine military efforts will be directed towards the Balkans, where there are plenty of easy victories to buoy an imperial government that depends on an image of the God-blessed, victorious Roman Emperor. All being well, I think the priority would perhaps be to first secure the Danube, before dealing with the Sclavenes within imperial territory. As with OTL, population transfers of defeated Sclavenes to Anatolia are quite likely. I can also see some Sclavenic warlords being allowed to remain within the Empire in exchange for conversion to Christianity, and a fairly "fuzzy" provincial system developing in the area, similar to that which existed in Syria in the sixth century with nomadic Arabs and Roman provincials.
If, on the other hand, Iran bounces back quickly, then there can be no reasonable doubt that all efforts will go to defending Roman interests in the Caucasus and northern Mesopotamia. The Balkans and Italy will continue to be largely ignored and starved of resources: perhaps not by quite so much as OTL, but both theatres will certainly be very much a side show. Constantinople's priorities can be summarised as:
1. Eastern enemies
2. Balkan enemies
3. Italian enemies
4. All other enemies
And this is pretty consistent throughout the Empire's history, certainly until the Komnenids, with only occasional aberrations: under Justinian, for example, you can arguably swap 2 and 3 around, although even Justinian spent a lot of money trying to fortify centres in the Balkans and not a great deal of money trying to reconquer the West.
Hope that this is helpful!
Thanks for the info on Byzantium. As you said the only way you could think of for Egypt to break away is with a rogue general. Let's say that happened would Byzantium be able to hold onto the Levant (with other external threats Arab raiders, Sassanids and steppe hordes)if it was to lose Egypt? As well, could Egypt while perhaps being culturally Greek, wouldn't the difference in language (Coptic) at least be a starting point for a possible rebellion.
In regards to Persia, after studying for a little bit and reading other posts the religion in the Persian plateau was still primarily Zoroastrian and would remain so until Islamization of the area by the Abbasids. Also without a millitary conquest it is doubtful this would change.
Addressing my earlier post about the Turks and their invasion of India, I wonder if we could see a stronger non Islamic invasion of India, akin to a earlier Mughal empire (without Islam). This could cause a larger Turkish presence in India, possibly with some territories of modern day Pakistan speaking Turkish (or some form of it). Turkish mercenaries will also seldomly be used aside from maybe in Persia(which could be interesting if they create a Mamluk type system; however unlikely with Zoroastrianism's aversion to slavery). Also, if any one has any idea on what religion would be dominant among the Turks, that would be very helpful. My bet though would be that they would be similar to the Mongols changing their religion to the area they conquer.
Also if anyone has info on the extent of Manichaeism in the middle east for the era, would be appreciated.