The notion of running slowly when nothing is happening and then responding when potentially relevant headers are detected and speeding up makes a lot of sense. This would be especially beneficial in environments lacking signals - which currently seem to cause the phones to go into overdrive seeking a signal. The effort fails and the battery is quickly drained for no reason. If nothing relevant is happening, the slow clock nap is a great strategy.
There is a sleep mode in WiFi which enables a client device to tell the AP that it will not be listening until it awakes and polls the AP. Since this discussion doesn't even acknowledge that capability, I'm skeptical of any of the rest of the claims within the article.