Actually, in Logic Pro 9, it puts the licensing info in the ProAppsSystemID and not the Logic Studio System ID. You can demonstrate this by removing the Logic system id and starting Logic. It will not ask you to reauthorize. If you remove the ProAppsSystemID and restart, it will ask you to reauthorize. But, if you have Final Cut Pro 7 (the new final cut studio), the ProAppsSystemID also contains it's licensing info, so if you remove it, you will have to reauthorize it as well - found this out the hard way.
24" iMac /C2D 2.8ghz/4Gb/320-7200/ Edirol FA 101 interface / OS X 10.6.2/ Logic Pro 9.1