Nope, and this is a too common mistake.
SAML on Discourse is not SSO, it’s just another login strategy, like Facebook, Google or Email/Password.
If you want to use it as the one true login, I really recommend implementing our native SSO protocol.
But, if you are felling adventurous, you can try to hack on the SAML plugin to add the SSO features one by one. I recently added the group sync feature from SSO to the SAML plugin.