If you just don’t use Notification Center, you can turn it off completely, which will also stop notification pop-ups appearing. To do so, open a Terminal window (it’s in the Utilities folder of the Applications listing) and paste-in the following, which is all one line:
launchctl unload -w /System/Library/LaunchAgents/com.apple.notificationcenterui.plist
Then log out and back in again to see the change. Alas, the desktop icon sticks around but it now does nothing when clicked.
To bring back Notification Center in future, again open Terminal and paste-in the following, which is again a single line:
launchctl load -w /System/Library/LaunchAgents/com.apple.notificationcenterui.plist
How to use Terminal on a Mac