I am four years too late, lol. An easier way for TS to check is to
1. shut off water supply,
2.drain empty the tank,
3. open back the water supply
4. lift the float to simulate full tank level

if water comes in from the outlet line, it means the check valve is passing.

All check valves will fail at some point in time. The either fail open or stuck in closed position.

This to me is a clever idea. When the mains pressure is higher than the pressure in the tank (which comes from the liquid height), it will supply water to the bathroom (or whichever tap that is taking water from the tank).
When the water pressure is low, or supply is cut, the water from the tank will flow to the bathroom tap. We all know the water from the tank can be rather low in pressure, which makes installing rain shower impossible.
A second check valve should be installed along the pipe supplying water to the tank so that the water in the tank does not drain down to your neighbour's house via the mains

The disadvantages of such set up are:
1. Water in the tank is hardly replenished since our mains pressure is/should always be high (in an ideal world).
2. Usage of check valves as a form of safeguarding is never a good idea, especially in a area as inaccessible as the tank under the roof.