The difference between Romex and audio cables is the insulation. Romex uses PVC (Polyvinyl Chloride) with a nylon jacket. Cables utilize a dielectric, or electrical insulator that is polarized by an applied electrical field.
Dielectric material varies in what results you will have, but it acts like a battery, in that when you send data or music via a cable that is polarized, the dielectric builds up a charge. Which is why some mfg - like AQ - add an actual battery, which places a DC voltage on the insulator itself, forcing it to remain charged in one direction only.
Power cable insulation (dielectric material) provides high polarizability. Creating an electric field which is called an "electric dipole moment". This means that the elementary particles (protons and electrons) are electrified; generally a molecular orientation that is active until it, well...it’s not. Timeline’s vary because not all cables are made of the same dielectric(s) and some are coated with other metals (think silver on copper) which, again, creates polarization curves. The shifting of these protons and electrons is the activity that settles over time. That is what you are hearing.
So, no, Romex does not need time to settle because there are no dielectrics being used in the insulation of the metals.
Hope this helps!