The question for the paranoid is whether it (the Echo) is useful enough while not connected to the Internet. (I think it's too much to expect any device to be particularly useful while off. :-) ) At least some commenters seem to think so—https://news.ycombinator.com/item?id=8568572, for example.
(Also, to be fair to chatmasta (https://news.ycombinator.com/item?id=8568265), I think that s/he was suggesting that the Internet connection / voice-recording function is on whenever the device is, not that the device itself can never be turned off.)