With GitHub (cloud version) specifically it doesn't (currently) work that way, you still need a "normal" GitHub username and password, and you do the organisational SAML login in regular intervals when trying to access that org's resources. I'm not aware of this being a widespread way of doing SAML, but I guess it supports certain use-cases (like keeping a GitHub identity despite switching jobs/OSS projects).
sources:
* https://help.github.com/en/github/setting-up-and-managing-or...
* https://help.github.com/en/github/authenticating-to-github/a...
[edit: formatting]