Unfortunately I don't think that I can answer this myself, but I can point you towards a book that might help: Decline and Fall of the Sasanian Empire: The Sasanian-Parth​ian Confederacy and the Arab Conquest of Iran by Parvaneh Pourshariati.

I've always been taught by my professors and Byzantinist peers that the war between Byzantium and Iran sufficiently weakened both of them, which in turn allowed for the Arabs to completely conquer the Sassanids and take 3/4 of Byzantium's territory, but I don't have a source handy that discusses this.

I think it depends on what you attribute to the war and what you attribute to other factors. Persia, on the eve of the conquests was a state wracked by serious internal religious divisions with the Zoroastrian faith reserved for urban elites but Nestorian Christianity being the most widely practiced faith, beside large communities of Jews and Manicheans. Politically after the assassination of Khosrau II by pretenders, the Sassanian government descended into anarchy, topped off by costly military losses to Heraclius in securing the peace. Even before the war with the Byzantines they had abolished their Lakhmid Arab client state which, when they eventually faced off against a large Arab invasion, meant that they had neither a military buffer nor a source of ethnic stability to their south. As if all of that wasn't bad enough apparently the entire region was undergoing an enormous epidemic of plague at this time.

Large battles like Qadissiyah notwithstanding the Arab conquerors apparently found themselves in possession of a country that was already in ruins or had been abandoned. The conquests themselves were largely in the form of "Ghazw," religiously inspired raids modeled off earlier tribal expeditions but instead of simply plundering they found themselves in possession of huge swathes of territory with relative ease.

Fred Donner's books on the Islamic conquests cover much of this material and would be a good start for anything on the Muslim conquests.

So in the absence of war, yes they would have been much stronger but there were enormous internal problems at the time that were only tangentially related to the war with the Byzantines.

Without a chance is obviously teleological, along the lines of asking whether the Byzantine Empire or the Roman Empire had a chance in surviving at all.

History (and especially war) is filled with chances that have to remain untested as counterfactuals, because we don't have a time machine to create a proper laboratory.

But with that said, I don't think anyone doubts that the Byzantine-Sassanid war had a catastrophic effect for both polities, not only because of the physical manpower costs of the war, but because of the weakening of the political bonds to the centralized state of both empires. With the Sassanids you had the political leadership in shambles from losing the war, and with the Byzantines you had major sections of their former eastern empire experiencing a full generation under alternate political rule.

Remember, the Arabs didn't besiege and conquer every city they came across by force. Cities negotiated with the Arab armies to preserve their autonomy and wealth given the relatively generous terms of the Islamic armies.

This would only have been possible if they viewed outside help from their former empire as remote in possibility, as well as the bonds of identity toward the old state as less than secure.