I wonder if good E2E encryption of the WhatsApp message rules out the app sending, in parallel, an indexed list of juicy keywords (encrypted or not) to FB servers for the purpose of targeting ads.
The cpu is not the most power-consuming component of your device: the radio and display both consume more power than the processor. According to [1], the cpu typically accounts for only 10%-20% of power usage.
However, a secondary stream from the app to a different endpoint would be detectable, so there are other practical challenges to the GP's scenario.
Couldn't it be a secondary stream to the same endpoint but using a different keying (ie, encryption with server's pubkey) mechanism (the metadata then wouldn't be E2E encrypted, but that's not covered in WhatsApp's E2E security page)?
Is that feasible client-side without burning all your battery?