Yes. A 3-core cable can supply a single-phase load. The three cores are then used as phase, neutral and earth. For an armoured cable, the armour is usually also bonded to earth as a separate protective path.
Using a 3-core cable this way is common for single-phase motors, pumps, lighting feeders and equipment fed from a distribution board. All three cores are the same size in the normal construction, so the phase and neutral conductors carry the load current while the earth core carries current only during a fault.
The cable must be sized for the load current and the length of the run. A cable sized only for the load can still be too small if voltage drop is high on a long run. A 3-core cable should not be confused with a 3.5-core cable, which has a reduced neutral and is intended for three-phase systems.