To reiterate, if you tick that iTunes support box, then, from that point on, every song dld (in a format supported by iTunes of course, eh?) that completes will be imported to iTunes. That is, if iTunes isn't launched, LW will open iTunes.
If it is the first ever song that you import that way (with the iTunes support feature), LW will create a playlist entitled "Limewire" (doh) and import the song(s) there. This results in you having 2 copies of the song(s): one in the Music folder and one in the Shared Folder.
If you wish to have LW open iTunes every time you click Launch on a dld, then disable the iTunes player in the Preferences, click Apply, quit LW and re-launch it (please, do not be offended by the way I write this. I do it only to make sure that a "heated debate" won't take place because of a slip). Every time you now choose a music dld (in progress or completed), click Launch and iTunes will open. If you have enabled in iTunes' preferences the copying files to Music folder when adding to Library, iTunes will also make a copy of the file in the Music folder.

__________________
iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

"Raise your can of Beer on high
And seal your fate forever
Our best years have passed us by
The Golden Age Of Leather"
-Blue Öyster Cult-