Apps do get removed completely but if you have synced it to your PC prior to deletion, when you sync again it will again be downloaded to your iPad. You can just check it so that it doesn't redownload. So it needs to be removed from iTunes also. The app store does keep a record of all apps that you have purchased, so if you delete in error, it can be downloaded again free of charge.
You can hide an app purchase also - go to your purchased tab in the app store and swipe the app, this will bring up a Hide option, just press to hide it. Hope this helps.
iPad 2 3G 64gb