Let me go out on a limb here and say you will be just fine, but....

Years ago, ALL home audio interconnects were a center conductor and a shield, with RCA connectors on each end. Since then, the studio practice of using a shielded twisted pair with the shield grounded at the audio source end has become standard, as this lessens noise pickup.

Your subwoofer cable, then, will be one step below Monster in its approach.

Here's the BUT: most RG-6 has aluminum foil, which is a great shield, and aluminum braid or a few strands of aluminum as a drain and second layer; quad RG-6 is double this. The problem is that you can't make a perfect metal-to-metal bond by soldering an RCA plug onto an aluminum shield. You will have to crimp an F-connector on it, then use an adaptor from F to RCA. A good crimp should be okay, but the hot lead's connection to the adaptor could give you a problem. I have seen these adaptors fail completely or be slightly noisy.

That is theory; in practice all should go well or there will be a 100% bad connection and you will have no bass. Realize that a lot of the problems that people cite with cables have to do with high frequency performance, of which there is not supposed to be any with a subwoofer.

If he also ran the westpenn cable, use it instead, as its construction is like the studio wires I mention above. Choose one of the conductors to be the hot, the other the ground, and solder those to a connector at the subwoofer. Do the same at the system end, but also solder the shield to the RCA plug at that end.