I assume that, with enough training, we could get similarly accurate guesses of a person's linguistic history from their voice data.
Obviously it would be extremely tricky for lots of people. For instance, many people think I sound English or Irish. I grew up in France to American parents who both went to Oxford and spent 15 years in England. I wouldn't be surprised, though, if a well-trained model could do much better on my accent than "you sound kinda Irish."