Hm, I was pretty sure if you clicked "Install" button Galaxy would re-download files. At least it was true for extras, there was a report in Mantis. And it's true for installers (yes, I separate them even though they're in the same section in Galaxy). I need to test it again. What files should I delete/modify in the game folder so that Galaxy could forget about the game and make "Install" button active again? Or maybe some modifications in registry is needed? I'm on Win 7 x64.
I'm not sure what exactly are you trying to achieve, but since your initial question was "Do you mean Galaxy will verify files like Downloader does before downloading..." then this is the case if you import the game folder using MORE -> MANAGE -> IMPORT FOLDER option. If you click INSTALL game will always install from the scratch because Galaxy is not aware of its existence of your disk.
As for removing game from sidebar without uninstalling it - the fastest way to do it would be to close the Client, rename the folder with said game installation, and restart Galaxy... This way it should disappear from the sidebar (once it happens you can - and should - rename the game back, to avoid breaking something with the installation if there are any references to it in the registry and whatnot).