Depends - if you pointed your desktop to the location in your home directory, then deleting or moving them will cause the desktop to lose them. If they were installed system-wide, you can delete the originals from your home directory - if they are elsewhere on the system and the desktop looks for them there.
I think some of your missing icons and control panel issues relate to the fact that permissions got screwed up like on your other thread. I dont know too much about desktops but that may be it. If you get the permissions straightened out (and maybe restart your GUI) some may reappear. With the rest, you'd need to reassign the paths to the system wide files or reinstall the icons if those were the only copies.