Why does anyone need identities when invoicing? Or more accurately, why must every invoice have an identity attached?
You will be able to generate and send unsigned invoices that has no identity attached.
But they are much less secure than signed invoices, because a "man in the middle" attacker could rewrite the Invoice so the bitcoins go to him.
Or if you have a dispute with the merchant and all you have is an unsigned Invoice, the merchant can claim that "your machine must have been hacked, you sent the bitcoins to an address that isn't mine!"