Yes, any two equal currents (equal in both magnitude and phase) flowing in opposite directions will cancel. Or indeed any net zero sum of currents in any combination of conductors. I.e. if all the conductors serving any device or combination of devices run together, there will be no net longitudinal current (as per Kirchhoff's first law.) The EMF radiation (and in the case of a signal cable, susceptibility) will cancel better if the two cores occupy the same line through space. This can be achieved by making them coaxial, or by twisting them together so that they orbit around a common centre line. Both methods will be familiar in applications such as aerial and data cables, but the same technique can be used in very critical technical environments to minimise the fields radiated by power cables.
With normal power circuits, it starts to become of interest when there are large areas enclosed within current loops due to wide spacing between the two conductors forming a circuit, and/or the current contains higher harmonics that radiate easily. In a domestic setting, this normally occurs with 'traditional' 2-way switching, and with single-core sheathed wiring where the line loops via the switches but the neutral via the lights.
When I was about 14, I installed some lighting wiring using surplus 2-core MICC. With multiple switched circuits and fixtures but only two cores per cable, I did some creative reassignment of the conductors as they passed through fittings, to minimise the total number of cable runs. Some carried net zero longitudinal current but others had slightly different currents in the two conductors due to serving different numbers of points. Some of the lights were fluorescents with wirewound ballasts, which create a peaky waveform. I soon found that switching these on obliterated all AM radio reception within 20 feet of the wiring. The fluos radiate by themselves, but the loop aerials formed by my 'optimised' wiring runs made them worse.
