No, the icon gets embedded in the game's code, so you don't have to include the icon file.
The problem with using a program like that is that it simply resizes an image multiple times to create the icon file. You see, an .ico file actually contains six or so images, depending on resolution of the original icon. This allow the icon to be presented differently when used in different ways (for example, the title bar of the game as opposed to the game executable's icon.) If you simply resize an image, it will probably be completely indistinguishable on some of the smaller settings, depending on the image you used. While I don't have a problem with people using it, by any means, I wouldn't use it myself, as it would result in a lower quality end product. I would recommend using a pre-made icon, or creating one in GIMP or Photoshop, which both have settings for easy icon creation. Maybe I'm just being nit-picky, though; I'll go ahead and throw the link up there in case anyone needs it. I'll admit there would certainly be times when it would be useful, especially if you're using an easily scalable image.