Highly unlikely. I understand this is what the OT required, but it is generally agreed the Jews had abandoned the practice long before this, just as they had abandoned similar rules for land ownership.
In fact, quite a few scholars contend these rules were never implemented, but rather were held up as ideals.
Both Philemon and Onesimus had Greek names. While this is not dispositive, it at least makes it more likely they were gentile converts rather than Jews. And Paul himself had made it very clear Jewish Law was not binding on gentile Christians.
Philemon lived in Colossae, a Roman/Greek city in Asia Minor. Jewish traditions with regard to slavery would have had no force of law there, assuming they had such force anywhere.
The relevant law code was either Roman or Greek, in which slaves were quite literally consider "animals that speak," and had almost exactly the same status as livestock. Under this law code owners could legally have a slave crucified on a whim. If an owner died mysteriously or was killed by one of his slaves, all his slaves, in some cases many hundreds, were executed.
BTW, if southern slavery was based on biblical precedent, what happened to the whole freedom after seven years bit?
While I don’t dispute that the practice of Levitical Slavery had probably been corrupted, the actual day to day practice is irrelevant to the discussion as it’s the principle that was laid down in Exodus that is important. Our belief in or practice of a point does not validate that point, it merely reflects on our own morality.
That being said, the idea that Jewish Law was not binding on Gentile Christians is only partially true. After all, Paul pointed out that we were no longer under the law, as the law had been fulfilled by Christ’s death, but His sacrificial atonement was for a covering of our sins and a transferal of His righteousness into our soul. This does not cover some of the other portions of the law dealing with daily life, which is also where a large portion of our legal code comes from.
In the case of Onesimus and Philemon, Paul was in fact reinforcing the idea that Onesimus must keep his pledge of lifetime service to Philemon, while at the same time reminding Philemon that Onesimus was more than just a servant now and to treat him as a fellow Christian. Roman or Greek law may have allowed something stricter than what Paul was saying, but that has no bearing on the situation.
Finally, I never said that American slavery had it’s roots in Levitical Slavery and instead pointed out just the opposite. Because of America’s sins of chattel slavery, and her refusal to repent from it, she was doomed to bloodshed long before the election of 1860 came around.