I doubt it. The Roman Empire alone at its height had a population of 50-90 million with roughly a quarter of that enslaved.

Even with extremely inclusive definitions of slavery (which are also not included in the classical count) the modern estimates of the total number of slaves is like 40-50 million. It's too many, obviously, but classical period Europe, Africa, and Asia alone would crush those numbers, and the 'New World" didn't appear out of nowhere when Columbus stumbled into it.