You can't back up directly to Glacier with Borg.
You can back up locally, then use the AWS S3 commands to upload to S3, or an "S3 drive" type script. From there you can use S3 lifecycle rules to move the files to Glacier. Personally I use a script to upload the files to Dropbox, because I wanted my backups in a different location / company in case my AWS account for some reason becomes inaccessible.
The backup scheme you suggested could waste disk space if done the simplest way. Borg and Attic both remove backup files in order to meet your configured backup schedule. For example it can keep daily backups for a week, then weekly backups for six months, then monthly backups. So over time the backup files created are removed on the local file system. If you archive everything to Glacier you'll have a lot of files in there that aren't actually needed. It doesn't hurt, but it will cost you money.
I don't have a great solution. You could sync your files, but this means if a virus or an accident and sync them you could lose your backups. My inelegant solution is to manually delete extraneous files occasionally, but this wouldn't scale. Interested in suggestions to improve it.
Update: I've published my guide to backing up from AWS EC2 to Dropbox, which would work for backing up to other destinations as well.