Does an action fire when adding a tag via the “Tags” meta box?

try to use undocumented filter pre_insert_term.

What you need is not a filter, but an action called before insert terms, i have not found WordPress have this kind of action.

for another way of thinking, you can use create_term or created_term action, although they are called after term created, if a user have no permission, we can delete the term they just created.