If a unit is damaged prior to playing Elder Dragon, will the unit die from Elder Dragon being summoned?

Yes, if an enemy unit already has damage marked on it, it will die the moment you play Elder Dragon.

Why this happens:

1. Passive Ability: Elder Dragon has the ability: "Any amount of your damage is enough to kill enemy units." This ability modifies the game's definition of "lethal damage." As long as you are the controller of the damage marked on a unit, that unit is considered to have lethal damage if its marked damage is non-zero (even if that damage is only 1).
2. State Check: Because damage persists on units until the Ending Phase (unless healed), the game state constantly evaluates whether any units have "lethal" damage.
3. Interaction: As soon as Elder Dragon enters the battlefield, its passive ability becomes active. The game immediately performs a check. If an enemy unit already has damage marked on it that was dealt by you (the controller of Elder Dragon), that damage is now considered lethal due to the passive ability, and the unit is killed.

Key Clarifications:

• "Your damage": This interaction only applies to damage that you dealt. If the damage on the unit was dealt by your opponent to their own unit (or by a battlefield effect controlled by the opponent), Elder Dragon's passive ability does not apply, as it only modifies the threshold for "your" damage.
• Timing: This process happens as soon as Elder Dragon enters play, which occurs before any reactions can be played to its triggered "When you play me" ability.

This is consistent with RiftJudge FAQ #10640, which confirms that Elder Dragon’s passive ability applies to damage already marked on units before it entered play, causing those units to die during the cleanup that occurs immediately upon the Elder Dragon entering the battlefield.