Does Vex Apathetic stun Baron if it is at Baron Pit when Baron is played there?

Yes, Vex, Apathetic will stun Baron Nashor when it is played, even if Vex is at the Baron Pit.

Reasoning

1. Programmatic Selection: According to RiftJudge FAQ #8685 and FAQ #9625, Vex, Apathetic's ability uses programmatic selection to identify the unit played by the opponent. Because the ability automatically selects the unit based on the trigger condition ("When an opponent plays a unit") rather than requiring the controller to manually choose or target it, it bypasses Baron Nashor's protection ("I can't be chosen by enemy spells and abilities").
2. Trigger Condition: As long as Vex, Apathetic is "at a battlefield" when the opponent plays a unit, its triggered ability will activate. This is confirmed by RiftJudge FAQ #9240.
3. Result: When Baron Nashor is played, it triggers Vex's ability. The ability resolves, stunning Baron Nashor and applying the restriction that it cannot move for the rest of the turn.

Sequence of Events

1. Playing Baron Nashor: You play Baron Nashor (which adds the Baron Pit token and places Baron Nashor into it).
2. Trigger: Vex, Apathetic’s ability activates and is placed on the chain as a Triggered Ability.
3. Chain State: The chain is now Closed.
4. Resolution: The chain resolves (LIFO). Vex, Apathetic’s ability resolves, programmatically selecting Baron Nashor, stunning it, and applying the movement restriction. Baron Nashor remains at the Baron Pit.