If Crescent Strike is played on a battlefield, then a unit ambush to the battlefield does that unit still take damage?

Yes, the unit that enters the battlefield via Ambush will take 1 damage from Crescent Strike.

According to RiftJudge FAQ #9516, Crescent Strike selects "other enemy units" at the chosen battlefield based on their characteristics (their location and controller) at the time the spell resolves.

Here is the sequence of events:

1. Crescent Strike is played: You choose a battlefield and one primary enemy unit as the target. The spell enters the chain.
2. Ambush occurs: Your opponent plays a unit with Ambush to that battlefield. Per RiftJudge FAQ #9326 and #9978, units enter the battlefield immediately when played and do not allow a reaction window. The Ambush unit is now present at the battlefield.
3. Chain resolves: The chain resolves (LIFO).
   • Crescent Strike resolves.
   • It deals 4 damage to the originally chosen primary target.
   • It then checks for "each other enemy unit" at that battlefield. Because the Ambush unit is now present at that location and is controlled by an opponent, it meets the criteria and is dealt 1 damage.

As clarified in RiftJudge FAQ #9516, the "other enemy units" are not targets of the spell, so the Ambush unit does not need to have been present when the spell was initially placed on the chain to be affected by the 1-damage effect.