Advisable, no. iTunes can get confused if the music is not where it was originally installed.
If you feel you must, then you need to completely uninstall iTunes. Then go to the My Documents folder and remove all your music. You MUST have a backup somewhere, NOT the iPhone. You can use the portable hard drive in a similar location. You then install iTunes again, this time pointing to the portable drive as the music location. You then hope the portable drive doesn't fail/break/become unreadable. And in the event you want to import more music, you MUST be able to point to the portable drive as to where to import the music. If you ever open iTunes and the portable drive is not connected, iTunes will fail and forget where the music is stored.
Really.
It can be a major PITA.
More information is at the iTunes site.
portable hard drive/ is it possible and how? Thank you!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic