Can the purple vex stun Nash?

Yes. Vex, Apathetic's ability stuns Baron Nashor because "Stun it" programmatically selects the unit that triggered the ability — it's not a choice, so it never targets. Baron's "can't be chosen by enemy spells and abilities" only blocks targeting effects (Rule 355.10.c, 355.10.d; FAQ #8685).

Sequence: your opponent plays Baron → Vex's "When an opponent plays a unit" trigger goes on the chain → it resolves and stuns Baron, also locking it from moving that turn. Contrast: an ability that says "choose/stun an enemy unit" (like Vi, Peacekeeper's) would fail against Baron, because that's a real choice and thus a target (FAQ #10502).