By default, this is not true because sox will use a higher bit-count and perform dithering when converting to a lower bit format (ref http://blog.beatunes.com/2014/04/does-24-bit-audio-matter.ht... ) in order to remove the extra bits while reducing the impact on dynamic range.
In all fairness though, this is the same argument used in the Xiph article ( http://people.xiph.org/~xiphmont/demo/neil-young.html ) in an attempt to justify the use of 16-bit over 24-bit, the prior allowing for a comparable dynamic range with the use of appropriate dithering techniques. I just think it's important to note that the process used with sox is doing more than simple arithmetic bit-shifts/multiplication.