There are two considerations: the Application file and then all the additional files Logic uses:
Application:
Yes, you could store the actual Logic app (or Final Cut Pro app) outside the Applications folder and even on an external drive. However, the file itself is not that big (1.3GB) compared to other additional Logic files. Also, the system expects the app to be in the Applications folder, at least for any update procedure.
Additional Files
Besides some Preferences files that have to be on the boot drive, it was always possible to store the sometimes huge sound libraries on an external drive. Although it is still possible (and there is plenty of information on the net how to do that), with LPX it is getting more complicated, because of certain expectations Logic has were it can find files and where it is looking for them.
Hope that helps
Edgar Rothermich - LogicProGEM.com
(Author of the "Graphically Enhanced Manuals")
http://DingDingMusic.com/Manuals/
'I may receive some form of compensation, financial or otherwise, from my recommendation or link.'