are your current speaker wires running parallel to your power wires? if you aren't getting interference now then it shouldn't change with new wire. But i wouldn't ziptie those together, i would zip tie them separately. and try to keep the speaker wire separate from power the best you can. I'm not an expert but i would think you run a higher chance of interference trying to fish your speaker wires clear across and under the dash from the passenger to drivers side in the front. So in other words, power wires and front drivers side speaker wire on the drivers side, and the rest on passenger side.
In my mind you are less likely to get interference through a speaker wire that a rca cable. You could always just leave lots of wire for that one run and mock it up, if it doesn't work just run it on the other side, if it does work cut off the excess wire and you're set.