I have not tried it. Yes, cable management is a problem.
Power cords can have a big impact on the sound quality of a component. Also, the flow of electrons (the more the bigger the effect) create a magnetic field around them and electrons are effected by magnetic fields. So I would think this would not be good. This is probably one of the reasons high quality power cords make such a difference. So, it strikes me as this would have a negative impact. I always try to keep mine from running together and only have them cross at right angles when possible. Definitely not always possible.
Maybe someone has done some experiments?