No, for a couple of reasons:
Yes. Backups which have already been configured will continue to work normally. If TKLBAM can't reach the Hub it just uses the locally cached profile and S3 address.
Yes - manually. It just won't be as easy. You'll need to do a couple of steps by hand:
transfer the escrow key to the restore target.
This means you'll need to have stored the escrow key somewhere safe or be able to create it on the backed up machine.
specify the S3 address and the key manually when you restore.
For more details see the tklbam-restore documentation.
Yes - but only manually. Just remember the Hub won't know anything about these backups so you'll have manage keys and authentication credentials by hand.