If your crush is filtering correctly, doubt it does anything extra. Can't hurt anything I wouldn't think. I use a copper manifold, so what do I know.
How does having a braid and a false bottom cause inefficiency? My thought was that the braid would filter any particles that went through the false bottom making a clearer wort. I didn't think it would prevent sugars from getting rinsed. But I've been brewing for about 2 years so I don't know