Slaves were excluded from participation in Olympic Games in Greece. Women ere also excluded except for equestrian women who owned horses. The Games were reserved for Greek men who were freeborn.
There is still scholarly debate about the role of a priestess, specifically the Priestess of Demeter, the goddess of fertility. Some hold that she was the only female allowed to be present at the all-male participant/spectator games. Others hold that the Priestess and young virgin women were both allowed to be present as spectators.
In other words, if slaves were not permitted and if only one priestess, the head Priestess of Dementer, was allowed in the Games and sat upon the dais, then there can be no scenario in which they would have interacted unless the Priestess were to be served by a slave who was there not as a spectator but as a serving person.