Andrew, This relates more to your prior post, and you are correct not to pull the wires together. Although the coax is shielded, it is not a 100% shield. The shielding drops down if the shield gets damaged (such as from pulling it through a wall) or when you go through coax connectors.
Also, you can get some large voltage noise signals on your AC line which can affect the relatively low voltage signal on your coax.
You will get more coupling and interference between two wires if: (1) They are very close together, and/or (2) They are parallel to each other.
I don't know the electrical code -- just the practical and theoretical considerations.
You're doing the right thing to pull them separately. Good luck! --Billy