I'm an RF design engineer, no avionics experience, but I have spent the last 5 years stopping HF radios and now mobile phones from interfering with themselves (insert innuendo here....)
Gengis, the big problem with practical faraday cages is you need to get in and out of them, and their weak spots are always the doors, hatches, lids, etc. You can try and seal them with a conductive gasket, but these tend to be fragile and don't take to repeated opening and closing well. Also as lunkenheimer says, there is no protection against magnetic fields.
QAVION, I don't know anything about how ILS systems work, but I suspect that a portable ILS tester will have a range of around 100 meters. Radio waves decay by an inverse square law, so that when the signal from an ILS tester reaches an aeroplane on approach, the signal will be below the noise floor of it's receiver. Even if it wasn't I suspect that the genuine ILS transmitter would swamp any ILS test transmitters, by several orders of magnitude, and the chances of interference there are minimal.
As to the radio waves propogating round the aeroplane to the ILS receivers under test I suspect that there may be a bit of bending, or fringing. I think it operates at around the same frequency as FM radio, and that isn't particularly line of sight . To be honest I'm getting out of my depth here as I've not touched an antenna design, or anything to do with propogation since university. Once again though the caveat that I know nothing about ILS, so if I have missed something fundamental please let me know.
EM interference is a strange unpredictable business, and you cannot easily predict how things will interact with each other. In other words, switch it off. And it's a top excuse to not do any work while travelling!
Cheers
John