IIUC North Africa was Coptic Christian and thus was persecuted by Byzantine authorities for their failure to embrace orthodoxy. If a Coptic Empire could be formed then perhaps it could it survive and thrive, but it would be unhappy and thus fractious under Byzantine rule.
"North Africa", which in this context I understand to exclude Egypt, was always strongly Chalcedonian Orthodox. Attempts at compromising with the Monophysite churches of Syria and Egypt by the Emperors of the seventh century were most strongly resisted by the bishops of Africa. There were odd Christian sects in North Africa earlier on who faced a degree of hostility from the Roman state, but these had ceased to be important by the fifth century.
As for "persecution": there's no real evidence that actual persecution really happened. I did my undergraduate dissertation on Egypt in the sixth century, and from that area, the very heart of Monophysitism, there's almost no evidence of the imperial authorities systematically attacking anti-Chalcedonian churches.