does watcher affect baron

Yes — Thousand-Tailed Watcher affects Baron Nashor.

Watcher's play trigger gives all enemy units −3 Might (min 1) without choosing or targeting anyone. Baron's "I can't be chosen by enemy spells and abilities" only blocks effects that target him (Rule 757), and Watcher's ability doesn't choose any unit — it's resolved programmatically at resolution, like Cull the Weak (FAQ #9385). So Baron, if he's an enemy unit when the trigger resolves, drops from 12 to 9 Might for the turn. If Baron's Might were already low enough, the "minimum of 1" floor applies as usual.