If there is damage on a unit, will it still die if I play Elder Dragon and bounce it?

Yes — the damaged enemy unit dies the moment Elder Dragon enters, and bouncing Elder Dragon afterward won't undo it.

The passive kicks in as a state check immediately upon Elder Dragon entering the battlefield: any enemy unit with even 1 of your damage marked on it becomes lethal and is killed in the cleanup that runs right away — before you even get priority to respond to the "When you play me" trigger (FAQ #10686, #11834). So there's no window to bounce Elder Dragon first and dodge the kill.

Once the death has happened, returning Elder Dragon to hand doesn't resurrect the unit — the lethality of already-marked damage doesn't retroactively disappear (FAQ #9875). Two caveats: the damage on the unit must be your damage (marked by you), and the unit must be an enemy unit. If it's your own unit, Elder Dragon's passive does nothing to it.