Why do you need to download and install Windows Installer Cleanup? What you describe is EXACTLY what Windows provides already through the Control Panel.
Start menu > Control Panel > Uninstall A Program
(in Windows 7)
Even in early versions of Windows, the capability is there and the menu drill down process is there too. The only difference betweeen doing what I described in Windows 7 and doing it in an early verion, WindowsXP for example, is the titles of some of the menu links may be slightly different (there may be a couple more steps in the ladder to click on)...but you get to the same place, i.e. the Uninstall menu. The Windows Uninstaller Cleanup is just using the Windows Uninstall menu FOR YOU instead of you using it yourself. You can do the exact same thing yourself by accessing the Control Panel from the Start menu.
I see no need to download and install another program to do this for you (unless there is some wonderful feature of Windows Installer Cleanup that you haven't mentioned yet).
What you suggest as a solution to the problem should work; however, it seems to include the unnessessary step of installing a program to do it. Honestly, both methods should work. In my opinion; however, the fewer unnecessary programs you have on your hard drive the better.
P.S. iTunes 11 seems to be a significant change to what iTunes 10 was. I recommend looking into reviews and descriptions of the newest version of iTunes BEFORE updating it. I'm still getting used to iTunes 11 and I'm not sure I like it yet. There are quite a few things about iTunes 10 that make me wish I'd kept that version.