Also, storing the data until it's plugged in would require an unusually large amount of storage, and that would be detectable.
That aside, speech recognition isn't that heavy of a process these days if all you're looking to do is extract keywords. We used to do industry-leading large vocabulary continuous speech recognition on a Pentium 133... phones these days are way beyond that without breaking a sweat. Detectable? Sure. But remember, I was talking about this person's plan to look at network data.
Furthermore you don't need to store all data. You can store only when the phone is hearing stuff, as determined by a super lightweight measure of magnitude that does no speech recognition whatsoever. Is the storage detectable? Sure. But again, what was I responding to? Network traffic monitoring.