Hmm. If you copy the library across from the one machine to the other, as well as moving the external drive, then yes. It should work. Personally I prefer to integrate the library and the media folder on the external drive which makes backing up and subsequent moves more straightforward. The normal layout would be something like <External>/Music/Media for the media folder with the .musiclibrary in <External>/Music. With a split library should you ever start Music when the external drive isn't ready the media folder can be silently reset to a folder on the internal drive, which leaves you the task of reintegrating everything down the line.
tt2