Dont want to tell anybody you shouldnt but a coil can get pretty hot and you want to keep it cool. So covering it is not a good idea even though it does look cool
This has come up before and as stated on those previous occasions wrapping a heat conductive layer of aluminium around a coil is hardly likely to cause it to overheat, particularly when the outer casing of most coils are made from an aluminium alloy any way. If you wanted to get really picky then you could argue that you may actually be trapping a very small layer of air between the outer surface of the coil and the inner surface of the coil which in itself could act as an insulator, but then that a very thin layer of air and therefore a rather thin argument too!!

Granted wrapping something with insulative properties such as plastic or foam around a coil would not be such a good idea, but a metal can really shouldn't cause you any problems. It's quite a common styling mod after all and I've never actually heard of anybody reporting a damaged coil as a result, I've had one fitted over my coil for over a decade now and with no ill effects.