Would there have been regional Latin accents in Roman times?
Obviously, voice recordings in any language have only been possible since the late nineteenth century, but have historians and/or linguists reached any consensus on how Classical Latin would have been pronounced, and if, for instance, accents in Rome would have differed from those in Britain, similarly to modern global languages?
That's a safe assumption. The Roman Empire, that covered a vast area across three continents, was composed of many tribes, nations, immigrants, isolated language pockets, and people with heterogenous educational backgrounds. Language learning books were not widely accessible, literacy was not ubiquitous, dictionaries with IPA not a thing and no Roman Broadcasting Corporation was able to push a particular standard. Plus: consider the long time the Roman Empire existed. I think it's fair to say that no language is static over such a long period of time. Over time, Latin, vulgar Latin to be precise, developed many different accents that eventually perhaps became crystallization points for the Romance languages.
Let me add, that scholars are pretty confident that they have reconstructed the pronunciation (that's different from mere accents and pronunciation of vulgar latin) of classical Latin fairly well. Here and there some features are still subject to debate, but nothing major.
I recall having read a contemporary account of the North African Latin accent from Carthage/Neapolis near the modern Tunis saying that, much like the much ballyhooed new Duo Latin course, failed to distinguish between short and long vowels.
That is the only such account that I can recall having read off the top of my head. It is interesting to wonder what modern languages would have developed had Vulgar Latin continued to be widely spoken in Northern Africa through the Medieval and Renaissance eras.
It would have been somewhat worse than British to American English. That's why Spanish, French, Italian etc. were able to develop in such a short period. The main linguistic breaks follow closely along natural borders. The people East of the Pyrenees but North of the Alps spoke the Latin that became French. The People west of the Pyrenees spoke what became Spanish and Portuguese, and those South of the Alps spoke Italian. Islands like Corsica, Sardinia, and Sicily spoke modified dialects of Italian and French as they were further isolated from the larger linguistic community. In the Oxford Latin Dictionary, there are hundreds of words from Gallic, Celt-Iberian, British and Native Italian descent which probably were regional. Using a Gallic based word in Italy probably wouldn't have meant much to them. Some Italic words would not carry to Britannia. The catch is that Italians were sent out to each province to govern, so there was a pretty centralized source, even if the locals couldn't get the words quite right.
Oh I could never forget Romanian, I did not mention it as it is one of the smaller descendants of Latin. But far from the least important, I believe it is the only one of the Romance languages which maintains the neuter gender. So it definitely has something that makes it special. : )