From my experience with the paper towel mod I assume that using wire would have a similar physical affect on the pads. The rolled up paper towels, when stuffed underneath the inner lining of the pads, pushes the padding out away from the driver and creates a few more millimeters of space between the driver and the surface of the pads. It also makes the pads a little stiffer because the memory foam inside the pad is compressed from the inside and pushed outward.
This is just an assumption on my part, but the paper towels because of their nature have a slight dampening effect on the sound quality as some have noted that it reduces bass. I imagine a rubber coated wire wouldn't affect the sound in the same way because of its consistency.