I have both and very rarely do I ever need to use either. The only time Authenticator usually stops me is when I disconnect and I have to log back in manually (the old way, not from the launcher), and TBH, it hasn't as of late. Even when my comp restarts, it rarely ever asks for Auth.
So unless you use a ton of different IPs and/or computers, nothing really changes except you get a ton more secure.
Good lord, could you imagine the former?