"If you convert an 8 bit image to 16 bits and do a lot of editing while in 16 bits and then convert back to 8 bits you will get a smoother levels plot than if you did everything in 8 bits. This indicates you get some advantage in doing this, but not the same as starting with a 16 bit image."
Only if you've got dithering turned on for the 8 to 16 bit conversion, which, in effect, adds a small amount of noise, thereby smoothing your histogram. That dithering can cause problems in matching tones, making it all but impossible to produce an exact numerical figure.
The only time where it's any kind of real advantage to converting 8 to 16 bit is when I'm going to add computer generated imagery - gradients in particular - to an existing image. Other than than, it's pretty much wishful thinking that it's going to help you in any meaningful way.