"Harvesting ambient radio waves can collect on the order of tens of microwatts of power. But sending data over Wi-Fi requires at least tens of thousands of times more power [..]"
So store it. Charge a capacitor for an hour, transmit for 0.1 second (adjust scales accordingly). If you're talking things like thermostats that are monitoring data that really doesn't change much over an hour or so, not a problem.
I've been waiting to see ambient-power products like this since I built a crystal radio when I was 8 or so. Powered entirely by AM radio waves, no problem with listening volume.
So if for every second you transmit you need 10^4 seconds of gathering energy, that means you can transmit just over 3 times an hour for 0.1 seconds. That is assuming perfect storage efficiency. But remember that to transmit over Wi-Fi you need to associate with the AP, obtain an IP address, discover where you are sending stuff (DNS resolution, routing, etc.), receive an ACK, close a connection, disassociate from the AP. Most of the timing of this is going to be dependent not on you but on the other end of the transmission. And if you are transmitting this infrequently, what percentage of time can you afford to have your data lost? Sure, you could optimize the heck out of this by using pre-defined routes, fixing the IP addresses of everything, using UDP to not have to wait for an ACK. I have a feeling you'd still need to actively run the radio for at least a second or two, which now brings you into the territory of transmitting only about 5 times a day.
But all that aside, the biggest reason I think running Wi-Fi off harvested energy is BS is because we are skipping an important step here: nobody is running Wi-Fi off watch batteries yet, and those are much more energy-dense than the typical radio spectrum. That's like seeing a Kickstarter campaign that claims to be able to run a mid-sized sedan off a rooftop solar panel: it is impractical bordering on impossible.
As an alternative, there are lots of protocols other than 802.11 that can transmit at lower power and with lower time frames. With these you can gather all the data onto a bridge which will then talk 802.11 on the other side. Or, you know, just put in a AA battery.
