Of course not. I own a phone, whose battery lasts a month, I can call people and receive text messages. And its common knowledge that its not a good idea to bring any mobile device to demonstrations for example. In Germany they've been known to indiscriminately monitor all mobile communications at demonstrations and put the numbers on file.
Your communications can still be tapped, your ___location can still be tracked through cell towers, and remote malware can still turn your phone into a persistent bug.
I don't think there's much of an advantage to using a dumb phone. At least with a smartphone you can run apps that encrypt your communications.
