Back up MBP to save space?

If I were you, I'd consider a drive upgrade. For about $100 you can get a 500GB drive and enclosure from macsales.com. Clone your drive to the new one using the free version of SuperDuper or Carbon Copy Cloner, then swap the drives. It's easy and you'll be right where you left off. No need to get rid of anything, move anything, etc. Why get rid of files you want on your computer? I currently have a 500GB that I am filling up and I'm putting a 750GB in it.

 

If you're adamant about avoiding skiltrip's suggestion for an internal drive upgrade, then yes, you should partition the external drive. One partition for your time machine backups and one partition for things you're considering deleting off your internal hard drive.

Time Machine is a backup app, as such is does not make files readily available for normal use. Instead it makes files readily available to restore to the original place in the event that you destroy a file you need. It sounds like you expect to be able to delete your iTunes library and still be able to play your iTunes library music, because you have it backed up on Time Machine. That is not the case.

If you're looking to free up space you can consider moving files, you don't need constantly with your computer, to your other partition. In my case, movies take up a ton of space. I keep them on an external drive, still linked to iTunes for organization and access. I can only play them on my computer when the external drive is plugged in.