It's a cool idea, but your neighbors might not like you too much, that might cause a good case of EMI - ElectroMagnetic Interference. There's a reason why computers should have computer cases with paint that is made for computers to protect from EMI. This not only goes for this computer, but for other mods that don't use standard computer cases. However, with today's modern electronics I would suspect this wouldn't be too much of a problem, but it could if your neighbor still uses yesterday's electronics or that it still might cause somekind of problem with modern equipment...just act surpised if you hear your neighbor complaining about something interfering with his/her TV.
I was even told in an electronics class that airplanes flying over head might be affected by EMI.