What problems could be caused by putting mains water in to the pipe from a shared water tank?
Is the tank sealed? If it's open, you still won't get mains water pressure through the tank.

The other option would be to just bypass the tank - ie cut the pipes in and out of the tank and put a piece of pipe in to connect the pipes together.

Here in the UK, it's not usual (and might even be against the water regulations) to have a tank directly connected to mains supply. You need to have an air gap to stop water being able to syphon back into the mains. You might be able to achieve this with a check valve to stop backflow.

Basically, you don't want water from the tank getting back into the mains, as the tank water could be (or become) contaminated.