Yes you can. I've played WoW using an external HDD many times. You do not need to install it on the computer you plan to use it on, just plug in your USB and run WoW.exe and it should work.
Naklin
Nefarian
Posts : 1032 Joined : 2006-12-03 Age : 46 Location : Shanghai
Character in WOW Server: TW-Stormscale (雷鱗) Name: Naklin Guild: All Gear No Skill