Any energy that creates turbulence coming off an airframe is, if you follow the energy back far enough, coming from the engine and the thrust it provides. So, in the case of turbulent flow and vorticity, the energy necessary to "spin up" that air from rest is energy that's not available to push the airplane forward, whether the turbulence or vortex impinges on the airframe downstream or not. Having it impinge on the airframe just makes matters worse, as it disturbs and energizes air at that point and, if you trace it all back, that energy is coming from the engine, too. Ultimately, all that energy is dissipated as heat as the spun-up air molecules bounce into others and make them move around faster - an airplane passing raises the temperature of the air if moves through ever so slightly. In a nutshell, we're taking fusion energy from the Sun that fell on Earth millions of years ago, passing it through extinct plants and dinosaurs, and combusting reconfigured organic matter in which they stored that energy, so that we can push our airplane forward - and spin up and therefore heat the air through which it passes. Go team.
A hypothetical "no-parasite-drag" airplane would leave completely undisturbed air in its wake, and have perfect laminar flow over every square inch of the airframe. Even then, the work necessary to displace the air occupied by the airframe itself and then bring it back together again is energy that's sucked from the thrust of the powerplant, too.
As far as "bookkeeping" goes, I'd tally it with parasitic drag. Interference drag is usually meant to refer, I believe, only to drag caused by the flows around two objects interfering with each other and the drag rise that results, compared to the two objects alone - like where wings attach to fuselages, where wing struts attach to wings, etc.
You can also think of induced drag as the energy necessary to do the work of either lifting the airplane or throwing an airplane-equivalent mass of air downwards, depending on if you like Bernoulli or the downwash theory of lift.