If I hold a battlefield at the start of my turn, move all units out of it, then move a unit back in later that same turn, does it count as a conquer and trigger conquer effects?

Ruling: No. If you score a battlefield through any means, you cannot score it again that same turn. Since conquer effects are part of the scoring process, they will not trigger.

Nuances:

• This restriction applies regardless of how the battlefield was initially scored
• Moving units out and back in during the same turn does not reset the battlefield's scored status