Yup, do the ring tests as described in the OSG (round trip with cross linked conductors). That also allows you to verify the topology of the circuit with some tests at socket positions.
Yup, they will find a number of faults including that, disconnections, high earth impedance etc.
If you start at the CU, and get reasonable results there, the inspect a number of sockets at random, and use a plug in tester on the remainder, you should get pretty decent test coverage. Obviously if you turn up further faults as you go you can revise your test policy.