I think you might be ok with a metal case… I believe one of the reasons the springs are mounted in metal/steel cases/tanks is to act as a sort of shield from outside interference. I believe where you have to be careful is in the wiring between the tanks and your module as the recovery amps are very high gain and can amplify noise or hum picked up over the wire if it’s passing next to a power source for instance… it may be necessary to use nylon spacers and screws to make physical separation between the tank and your case assuming the metal case is also 0V (“ground”) but I don’t think so as if I remember correctly when putting my Neural Agonizer together the reverb tanks also provide a “ground” connection.
Some other info here:
http://www.tellun.com/motm/diy/tln156/TLN-156_User_Guide.pdf
Worst case, you could build up the Belton brick section of the Music Thing Spring, too, and connect that, though this is not ideal as vinc mentioned. I say try the tank! As vinc also mentioned they are fun to play (tap, scrape, pluck) on their own if you have it outside your case.