You misunderstood me. The bones could be the bones of a persecuted Christian from before the time of Constantine reburied in the church as a relic of a martyred saint and these bones would be a few hundred years older than the church that was probably built to house the bones.
That is certainly possible. The point I was trying to make was that the Roman Empire was not persecuting Christians in 5th Century. It was at the time trying to fend off invading barbarian hordes. By 476 AD the Western Empire fell.
I would think the archaelogists who found the bones could determine the age of the bones and therefore whether or not your theory is possible.