I heard that Correct Connect doesn't actually connect you to the Internet. It just monitors the connection to see if you are. As you discovered, you don't need it.
I would suggest keeping it installed, but removing it from the startup group. If you do later find that you need it, you can run it from the Program menu.
I use it, but it doesn't seem to do anything useful. If my connection goes down, pressing refresh does not nothing. Unplugging the modem power suppy and plugging it in again re-established the link OK, whether I press refresh or not. Reconnection seems marginally quicker if I press refresh, but I wouldn't bet on it.