And Tunisia/North Africa doing that with Latin just seems ridiculous. If you're a nationalist speaker of a Romance language in North Africa, why would you want to make your language more Latin considering the whole Carthage thing? Especially when Carthage is likely to be a major city in North Africa. We can tell from 4th century texts in North Africa that local soldiers (amongst others) had a very deviant form of Latin which was influenced by the Punic which was their native language.
Having Arabs/Muslims speak Latin was mentioned earlier. This would have to be in the 12th century or so when African Romance and Punic were finally extinct and the region was essentially purely Arab. But assuming you can enforce on the Arabs to speak Latin (why--if they have to be Christian, why make them speak Latin, or even for any other reason, why make them speak Latin?), they'd have their own pronunciations. As we can see with English pronunciations of Latin and other regional pronunciations, it would not be like the Latin of the Roman Empire. And in a few hundred years, that pronunciation of Latin would evolve into something different from what it was, as well as even further from the original Latin.