...no. An open network is unlikely to give reasonable doubt.
The forensics teams will just grab all your kit, image any media and then tear them apart. Not even things like "Truecypt" with their "plausible deniability" (which doesn't really work, BTW) can help. Even if that does prove to be uncrackable (which is *highly* unlikely) then there's all those lovely registry entries, temporary and log files to sift through.
Oh, and if you are in the UK, you *must* hand over your keys/passcodes when asked.
Moral of the story: if you are into kiddy porn, they will find you. It's just a shame the punishments are not more severe. Well, they might be if the other inmates find out you are a nonce.
Second moral: The above will probably change in a few years when forensics goes private in the UK. All you have to do is make is too hard to be "economic" for the forensics teams and their managers will tell them to stop. That's right, the boss's bonus is more important that justice. Don't you just love privatisation?