Can Thousand-Tailed Watcher reduce the might of a unit to 0?

No, Thousand-Tailed Watcher cannot reduce a unit's Might to 0.

According to the card's text and the corresponding RiftJudge FAQ (ID 3124), Thousand-Tailed Watcher's ability reduces the Might of enemy units by 3, but it includes a "minimum of 1 Might" clause. This means that even if a unit's Might would be reduced below 1 by the effect, it will stop at 1 Might.