I know it is possible to create SMS users via the Management API but is it possible for users to sign up on their own via the Signup API?
I tried a couple combinations but was unable to get it to work without providing an email and password.
The text at the bottom of the SMS Setup Dialog leads me to believe users should be able to sign up on their own.
Check this if you want to prevent sign ups to your application. You will still be able to create users with your API credentials.
