No, you can't add user tags to multiple users with API as this endpoint does not have the
additional_tags command. If you use the tags attribute in this context, the user tags of your call replace any tags that exist in the user's profile.
As a workaround, add a dropdown custom user field and add a tag to each value. In the API call, add the user field value for each user using the user_fields attribute.
Alternatively, you can update information for existing users through the bulk importing users feature.