I wouldn't bother with the added cost and time as a CFC is fairly efficient to begin with. At some point you are limited by the wall thickness of the copper and thermal conductivity.
with a relatively small inner diameter of the copper line, having a rifled or spiraled design, IMHO, just has more places for debris to build up and hide. The constant 360 degree turns creates a natural turbulence with the fluid moving through the turn, which provides plenty of activity to eliminate lament flow. As the fluid travels through the constant turn of the copper tube it will be moving with a swirl-like pattern, so the fluid in contact with the copper wall will quickly be swirled into the center allowing a turbulent flow.
The wire on the inner tube is to separate it from the outside tube, so that surface area is kept open to the cooling water flow. The benefit of the turbulence is very little in this instance, as the tube is already moving through a long radius turn.
Would it be more efficient? Possibly, but I doubt it would be a great improvement compared to the efficiency it already has. I think it would difficult to measure the increase of efficiency for the reasons stated above