Assuming that you mean what you're saying, and that the Empire survives without losing territory, then you've got a half-decent chance of the Empire surviving till modern day - assuming they maintain their strength.
It had a reasonably dominant primary culture that was creating a "Roman" mega-culture that would have been able to survive an ATL seperatist nationalism.
I've always maintained that the Caliphate might not survive a defeat by the Romans, but if it does, then they'll be just enough to prevent the Romans and Persians from attacking each other for fear the Caliphate intervenes.
Considering a surviving Empire might have the time to recover from the weaknesses created by Justinian - they could reconquer the Balkans, and encourage the Exarchate of Africa to peacefully integrate local rulers - and still provide the resources to back them up given a decade or two. Having Syria and Egypt will really help support the Exarchate. Even better is that they can finish the reconquest of Italia, and support Spania.
The could very well survive as an Empire that controls Italia, Spania, Africa, Egypt, Syria, Anatolia and Haemus (OTL Balkans). With no repetitive Arab wars of reconquest and the Persian Empire in no small amount of chaos, they have breathing room for a few decades/a century and can consolidate. Don't forget, this Empire has been getting battered and bruised for nigh on two centuries. This is their first breather.
Importantly, there is no Charles Martel in this timeline, or Charlemagne technically as he can't defend against an Arab invasion that doesn't happen. So no HRE. The biggest threats in the short term are the Visigoths in Spain - the Franks in France, Arabs, and Persians - once the Balkans and Italia are secured. There is every chance that if the Byzantines can rest - they'll be able to hold the territories, as they won't be obsessed with rebuilding the Empire to the cost of fighting the Visigoths and Franks - at best they'll try and take advantage of civil wars.
Additionally, if the Visigoths decide that they don't want to trade via the Byzantines, they can lead the age of discovery, which the Byzantines are now in a position to exploit.
TL;DR Yes, the Byzantines can survive till the modern day. Just let them have this win, reconquer italy and the balkans, and REST. They've not had a chance to rest/regain manpower since Theodosius. With their culture and territory, they can survive.