Total conjecture since I actively avoid signing in with services like Google or Facebook in most instances but I would say it likely depends on how the service X handles logins.
If it actively consults service Y during login, your login will likely break.
If service X stores it's own credentials, only initially receiving them from service Y or perhaps updating them only periodically, then they are less likely to break.
I think "email" login is the best example of the latter. After a verification email is sent, it doesn't matter most of the time if your email address is accessible or what have you, so long as you type the correct one into service provider X's login box with the right password, you're golden.