This seems to apply more to black market trade than the modern internet. Information can't be stopped permanently, but the usage of various services on the internet can be made less convenient and curtailed, even by 2nd and 3rd rate governments, if only for awhile. Meanwhile, the most powerful state on Earth can't stop the inflow of illicit drugs.
A tunnel large enough to walk though could send 10 people a minute without problem. While 24/7 would be near impossible to achieve, it’s 600 people an hour, 14,400 people a day, and up to 5,256,000 people per year.
see e.g. http://www.leica-geosystems.us/en/Tunnel-surveys_1693.htm
They probably wouldn't. But you also don't necessarily need GPS to do this. Have someone survey it topside, use that data and a compass underground.