You won't even be able to factory reset or even remove your account from an old Gingerbread device. Sounds like a huge security flaw right there.
>you will start receiving username or password errors and will no longer be able to:
>Sign in to Google products and services like Gmail, YouTube, and Maps
>Add or create a new Google Account Perform a factory reset and try to sign in
>Change your Google Account password, which signs you out on all devices, and try to sign in again
>Remove your account from the device and try to re-add it