Well, yes, but that implies no dithering.
Agreed, although dithering will "kill" the bottom ~3dB, so again not "bitperfect".
In any case, no-one in his/her right mind would use the constrained 16bit domain in a modern software environment making it all this a bit academic.
Still, it's interesting to do the calculations to get a feel for the absolute error margins. In Audacity I managed to lose almost 6dB to noise when also correcting for DC bias! All of this starting with a "perfectly" generated 20kHz 44.1/16 tone at 80% volume.
Bottom line: keep your source as is, use a proper player with enough bit resolution, and normalize to your hearts content on playback.