I don't think that Coriolis has much effect on which direction water spins as it drains
If you had an absolutely perfect toilet with an exactly circular bowl, no surface imperfections whatsoever, and a flush valve that distributed water into the bowl evenly forming no eddies, no ground vibration whatsoever, the moon was in proper alignment, and plenty of chicken blood for the sacrifice, you *might* see the coriolis effect in action. Aside from that, no, it has no noticeable effect on the way your plumbing drains.
And the proper cartridge would have to be something good and hefty. I'm thinking .45-70.