Earlier quoted context omitted.
I'm pretty sure Signal at least doesn't encrypt at rest on your phone. So the drive would have to be encrypted as well, which is not default on Android
Apart from that, regardless if you're on Signal or Telegram if authorities get hold of a protester's identity on such an app and have the power to access the app's servers they can gradually uncover social networks by reading metadata (if I'm not mistaken).
But as far as I know Telegram has no equivalent feature.