When you play Vi Peacekeeper, it applies a stun to a unit. Can this be done to Baron?

No, Vi, Peacekeeper cannot stun Baron Nashor.

Vi's "When I attack" ability requires you to choose an enemy unit to stun, which makes it a targeted ability. Baron Nashor's protection ("I can't be chosen by enemy spells and abilities") prevents him from being a legal target for that choice — even if he's the only enemy unit there. The ability will fail to find a legal target and do nothing.