iTunes won't exchange them automatically, though you can do certain steps to make things easier such as creating a playlist of items you are re-ripping so they are in one spot for deletion when you have made the copy.
I think even burned compilations will be remembered as long as you entered the metadata into the CD when it was in that particular computer. It is not kept on the CD but instead in a database on the computer. It just won't be in the Gracenote database to which any computer has access.
How iTunes remembers audio CDs - http://support.apple.com/kb/TA27785
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html - "iTunes Library Extras.itdb contains some Gracenote CDDB information."