What is an "open WiFi connection"? If WiFi is active in the router, it would have 254 addresses available, going along with IP protocols unless it was limited by the provider.
A device can't jump in without a password, assuming the WiFi network was set up to be secure and there's absolutely no situation where that should happen. If it was connected wirelessly at the beginning, it may be able to have 'auto connect' turned off.
There is also, absolutely no way a government should be allowed to access this info IF they have prevented unwarranted search or seizure.