If you update the territory on a Company it adjusts all the territories on linked records (e.g. Opportunities).

If you want to go down the route of doing a mass update via the database you can do this. Are you wanting to make the opportunities match their linked companies?

BUT!!! Do these opportunities have communications, quotes and orders? Will they need realigning as well?

I have just performed the mass update for companies and people and saw that it does update the territories for associated opportunities. Unfortunately this doesn't quite fit our needs as our territories are based on geographic location of each customer site where as the companies associated with the site might be headquartered elsewhere. e.g. A California vendor may be the customer for a site in Florida.

If I mass-update the opportunity territory field in the back-end database will that break other things?

You can do (oppo_secterr) but think about other associated records as well (communications, quoites, orders) as they will all need their territory (xxxx_secterr) fields adjusted as well