It's decent idea, phone usually use more battery when there's no strong mobile signal. I don't know how it can be implemented either, but i believe Wasabi team have sufficient technical skill to do that. Although i wonder how much battery can be saved when you use Wifi rather than mobile internet.
This option exists, but not so much to save the battery, but when it comes to updating applications, and the purpose is to avoid downloading too large files over the mobile Internet because these are often limited
by mobile providers with such data consumption.
As far as I know, multimedia is the biggest drainer of the battery, and in the mentioned Wasabi case, it would only be text communication, so that part should not be a problem for battery capacity. For the application, I assume that some kind of customized Tor bridge could do something like this with minimum requirements.