If the Byzantium looses Balkan regions from Croatia to Macedonia,they will obviously tighten their grip over the Levant,Egypt and Anatolia where the fleeing Greeks/Romans would be resettled.
Not really the case OTL, where Slavs conquered most of Greece and most assimilated into the ancestors of modern Slavic-speaking Greeks. The Byzantines had to re-settle the area with Anatolian Greeks afterwards.
But since this question is about ATL,would the Byzantines resettle Slavs into their empire is my doubt after their conversion to the Byzantine Church. This would help the rulers get their edge against other sects which they didn't like much. Also,since this empire now is now too Christianized(very universalizing religion) by the time of Slavs,Stillicho like situation as in earlier Roman Empire would possibly be avoided. So that would Strengthen Byzantines like anything. Now Persia would sense danger with this powerful Greek and Slav Superpower and could probably ally with their neighbouring Scythians/Sogdians/Massagatae or Tocharians or something who still existed then. Now that would be interesting. Zoroastrianism too could become an universilizing religion and this in turn would worry Christian Europe who could then react appropriately to unite or something as Zoroastrianism now containing Eastern Iranians and Tocharians come in a sufficiently fierce contact with any European empire either in the Anatolia or somewhere in Eastern Europe. In that case,a unity of Frankish kingdoms,Visigoths,Germans,Anglo Saxon England,Slavs,Balts,Greeks isn't that far fetched. So now Middle East would become a true mix of Europeans with sprinkling of Tocharians,Persians,Eastern Iranians who'd be converted to Christianity if they settle in European administered territories.
Religious disputes were bad enough in OTL Byzantium, so this could result in serious internal conflict, weakened military and civil instutitions, and open their country to invasion from the outside. The Copts OTL invited the Arabs in, and later revolted against them several times, so the Byzantines are certainly at a huge risk here of having similar events happening here. The Arabs will still be restless without Islam, and a good Persian ruler can smash them wide open. Same with the Avars or another steppe tribe. Western Europe is already lost to Byzantium, since IMO the Berbers in Africa and the Franks in Western Europe will push out Byzantine influence.
Best hope for Byzantium is a Sassanid collapse, but even that just means they get replaced by a Turkic dynasty (i.e. Seljuks)--they weren't all Muslims or invited in by Muslims, Uyghurs were Manichaeans, some were Zoroastrian or Christian, etc.--or one of their own nobility (i.e. Mihranids) and the state revitalised and ready for another major war against them. But by the 7th century times have changed and the Arab tribes will be a potent force in any conflict, as will steppe groups like the Avars, Khazars, Bulgars, etc.
Do you mean Arameans or Armenians?
No, I mean the Armenians. They followed Miaphysitism/Oriental Orthodoxy and maintained a separate identity from Byzantium despite centuries of Byzantine rule. You could attribute their success to them being on the borderlands between Rome and Persia and later Rome and the Caliphate, but large swaths of Anatolia remained Armenian from Antiquity to their deportation and destruction in the Armenian genocide (and concurrent emigration to other countries). They did not assimilate into Greek, Persian, Arab, Turkish, or Kurdish culture in any sizable numbers, although a lot of Anatolian Turks and Kurds are likely descended from Armenians (and Aramaic-speaking groups for that matter).
The question is why this wouldn't also be the case with the Aramaic-speaking peoples, who are in a borderland between Persia and Byzantium, have their own strong religious institutions, and a strong and ancient written culture.
I agree with the first part of your argument. The rise of the Arabs was indeed shocking to contemporary observers and later historians alike (including Muslim ones), and nobody really was likely to have predicted it in 600. Only in recent years we are starting to make real historiographical sense of that turn of events.
Not that it was unlikely in itself, but surprising to most of everyone involved, sure.
However, a (obviously more limited) spread of Arabic outside the peninsula was an ongoing process before Islam (we have clearly Arabic onomastics in Palmyra in the third century already; the inscription of En Avdat, with three lines of poetry in Arabic that are considered the earliest secure and roughly dated attestation of the language, likely from around 100 CE, was found in what is now Israel; and so on) that would likely go on even without the Conquests, at least in inner Syria, parts of Palestine and all along the Euphrates. You won't see an Arabic-speaking Tunisia ITTL, and probably Egypt neither; but for at least parts of Syrian and Iraq, it's still likely to happen.
IMO the most likely effect is that areas like Nabatea, Palmyra, and lower Mesopotamia become mixed between Arabic and Aramaic-speaking communities in the absence of Islam, except in the more desert areas where Arabic will supplant Aramaic (as it already had by Late Antiquity).
I wouldn't be surprised if in areas like the Western Desert of Egypt you saw Arabic-speaking groups, who might assimilate the locals Berbers, Tebu, or other peoples.