That's not how it works.
When you use SSO to auth the website never sees your account credentials.
The site: Google, here are my SAML codes can you auth this person.
Google: cool those SAML codes are correct, hey user what are your Google auth details?
User: here you go Google.
Google: sweet, those are valid. hey site here is a token specifically for you for this user.
Site: welcome user.
At no point does your Google password hit the site and the tokens for other services will not work with a random webapp.