Interesting thing to think about. If a cable is connected at both ends, a coil in the cable becomes an inductor. If one end is disconnected, it acts as an antenna. So the question about shortening the length is really the one to think about. Either way, the effect should be very small when there is no significant metal inside the coil.
One other thing to consider, if the cables are shielded, the inner conductors should not act as either an inductor or as an antenna. That is what the shield does, divert magnetic fields around the inner conductors.
The rats nest approach will still make a nice antenna, and probably a better one than the coil. Thats basically what they do with the antennas in our cell phones, they are all wadded up internally. They work better than the old "rubber ducky" antennas that were neat little coils encased in rubber.
Thanks for the food for thought..
D
"The best thing about building something new is either you succeed or learn something. Its a win-win situation."
--Greg Westbrook