Seems that the Earth's shadow is 1.4 million km, and the Hill radius around 1.5 million. That ratio won't be the same for different size planets, as they scale differently with mass, but I doubt you'll get eclipses in any plausible configuration.
The amount of energy that hits the surface in a year is what determines habitability. The effect of these eclipses is cumulative. It shrinks the habitable zone the more rings you out into such a configuration.