Profile: Add tag(s) to new contacts

I'd like to be able to add tag(s) to new contacts created via a profile. This is very similar to the "Add new contacts to group" feature in the profile Advanced Settings. Ideally the profile Advanced Settings page would present a list of all tags, and I could check the ones that I'd like to be applied to new contacts created via that profile.

Use case for this is to tag event participants as having attended that event, or to tag contacts that signed up for our mailing list via the standalone profile on our main web site.

I don't think I can use the "Batch Update via Profile" feature to do this inside CiviEvent. If I create a profile that has only the "tags" field in it, and then use that to batch update, I think the tags that I select will overwrite the existing tag sets for all contacts, correct?