Does using Emperor's Divide on a unit that is ready exhaust it?

No, using Emperor's Divide on a unit that is ready does not exhaust it.

According to RiftJudge FAQ #8882 and FAQ #7964, when a unit is moved by a card effect, its state (Ready or Exhausted) does not change unless the card explicitly states otherwise. Because Emperor's Divide does not contain text instructing you to exhaust the units being moved, they retain their "Ready" status upon arriving at your base.