It can be done, but I presume that the post-softfork nodes will treat the units of the system differently than the pre-softfork nodes. So different, that the post-softfork transactions will not be validated by the pre-softfork. Pre-softfork nodes will receive something like Alice sends 0 coins to Bob (with an extra note indicating that it's a softfork), and in post-softfork nodes, these 0 coins will be accompanied by some signature that spends new, post-softfork coins.
In the proposed soft-fork, pre-softfork nodes don't see Alice sending coins to Bob, since they will see *only* the coinbase transaction in each block. It will look to them like Bitcoin has permanently ground to a halt (with no coinbase ever getting spent either).
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.