The token changes each time the user logs in (I tested this). I assume this is for security reasons.
According to the comment you linked to, it’s because the token represents a user session (of sorts), not the user themselves. So, no, it’s not suitable for your purpose. Is there some unique (or reasonably unique) data in the response? usernames? id? email address? If so, you could combine this with the service name (e.g., “facebook”) to identify users over time.