Is it possible to due this being vacuum or pressure, yes but you would really have to want it. The cost would be insane, and the build time even longer. It is not easily feasible for any meaningful distance, unless it becomes a 300yr project or some crazy time frame. You could save tons of money resources and etc if you only had 1 exit/entry per block, and people just had to walk that far.
The tubes would have to be super sturdy to withstand the ground pressures and earthquakes. They are digging super tunnels in Europe for trains, but the whole project is schedule to take 2-3 years just to go 20 miles or some super short distance.
Once you used up the worlds supply of concrete you would have to develop an even more expensive material to complete the network.
You would have to have numerous automated locks, as in the panama canal, because pushing a 20 miles distance from one pump is probably impossible. The pressure requirements would take too long to build up, and be to high to be safe, and leaks.
However, if you had smaller segments and redundant loops leaks could be detected and routed around. You pass through a lock, and it already has a tank a pressure or stored vacuum waiting for you to use. Maybe you could some recycle some of the pressure for the next user.
Each segment would need 2 or 3 levels of redundant fans/vacuum pumps and power supplies to in case of failure.
I believe maintenance, the truly staggering amount of electricity needed, and resources needed to build it in the first place would be crazy. Also any kind of failures could leave large numbers of people to suffocate or die from CO2 with no viable way to exit to the surface. Any kind of emergency exit would have to have a crazy system of seals to prevent leaks and increase cost exponentially.