In the proposed soft-fork, pre-softfork nodes don't see Alice sending coins to Bob, since they will see each block as *only* containing a coinbase transaction.
Pre-softfork nodes could be completely unaware of post-softfork coins, correct. Whether there exist transactions with 0 coins sent, or just a coinbase transaction to old nodes, the result is the same. They cannot verify the post-softfork transactions.
What the proposal shows is that the notion of soft-fork is not as clear cut as it seems at first, and is really more of a spectrum, based on how much of the new rules are being verified, or even visible, to old nodes.
A softfork is change(s) so that the client is backwards-compatible. Maybe what's more of a spectrum is the definition of backwards compatibility. For instance, one might argue that being unable to verify a post-softfork transaction is not backwards-compatible, even if it technically is, because verifying all transactions is considered the normal state.