Have to agree with Styles here.
It's not a good idea at all.
One, there isn't anywhere near enough people capable of working together to achieve such a thing.
Two, the tech no longer exists (if it ever existed) in the Fallout world for hollowing out huge underground caverns and drilling massive interconnecting tunnels. If it did, it wouldn't work anymore. If it worked, no one would no how to use it. If someone knew how to use it, why would they drill a tunnel to a place they've probably never heard of?
Three, why?
We have the technology to build the tunnels at least.
http://fallout.wikia.com/wiki/Find_the_excavator_chip
What is probably missing though is the practical geological survey skills. IANAG but not all ground is the same, some is soft and squishy and some is hard as a preverbial rock. Some bits are hard to dig through, some bits are silly to dig through as they'll collapse or let in water.
But I agree with the rest - it doesnt make a lot of sense; why would people build an underground railroad when there are many more pressing matters, and if a transport network is required in a somewhat civilised area, it can be done a lot cheaper and easier on the surface. You tend to go underground where going overland is Geographicly difficult (Very Steep hills and mountains, Urban Areas, The English Channel) enough that the surface becomes unfeasable.
The rest of the OP kinda sounds like Fallout 3, except more of it....