Interesting! I'm not sure to be honest. I imagine in practice it's hard to get a pure twist without any bending, and if the system can't detect any difference with a twist then the need to detect it is also nullified as it is effectively the same system.

Maybe with polarization maintaining fiber? If at the gap they are aligned a teist will make them more perpendicular reducing mode coupling.

Disclaimer: I know nothing about this field but have spent a lot of time in a dark lab surrounded by various types of optical fiber.