Fun experiment for you kiddies: Put a 3.5 floppy on top of your monitor and hit the degause button 50 to 100 times... Guess what. The disk will be fine. Just dont be MOVING the disk WHILE you are hitting the degause button, that will ---fudgesicle--- it up (magnetic flux).
BTW Aluminum is a good electrical conductor as well as a good EM inductor, so it should work well as a faraday cage. If you are REALLY worried about data loss, get an old steel food can (one big enough to put the drive in) and use that. Hell, even better, shield the monitor, and any potential interference to anything (not just HDDs) will be eliminated.
No offense, but people worry way to much about a very small amount of EM way too often. But I guess it is better to be safe than sorry. (Also, used steel food cans cost nothing, but you have to actually BUY sheet metal...)
EDIT: No matter what you decide: A faraday cage has to be grounded to work properly. The point of it is to absorb EM and convert it into electricity. If grounded it can "vent" the electricity (doesn't really work quite like that, but the cage needs to be grounded to work fully).