If you are talking about something like openauth (where you sign into some random website using your Google account) yes, but your base identity is still tied to Google. So if Google goes down, you lose your google account, and you also lose your account at every other website you logged in to using your google account.
Yeah, essentially that. The back-up plan in case your instance goes down is a separate issue, my main plan is just that users shouldn't need a new account for each fediverse application they want to try, considering one account is already able to make any kind of post.