flommer - you're thinking in the right direction. You're right that converting from 24 to 16 bit w/o dither simply hacks off the last 8 bits. Similarly, when converting from 16 to 24, 8 new bits get simply "hacked on."
If a bit was 1111111111111111, it's 24 bit form will be 11111111111111110000000. The bit stream it's a part of will sound exactly the same. However, if you process it in any way, you'll benefit from the ability to store the result of the math 256 times more precisely.