Hiding the extension doesn't remove the extension. It just hides it, which, by the way is a very bad idea IM(not so)HO.
You can show the extension and then edit the file name to remove the extension. You know you've got because Windows complains. That does work. I just tried it (Windows 7 and FileZilla). You can also remove the file ending after you upload. I just tried that too. It works too. The reported file type changes to 'file' on my server, but it is still just a plain text file.
Why are you trying to do this? That extension can be important. Please explain :)