SoL, yes that's what happen when you push 5 stops in post.
I only know from other electronics, so not sure if it maps 100% on cameras, but most signals can be less-noisy, the earlier you amplify it. So in your case, you amplify early (ISO3200) is better than in post.
Good example is the satellite dishes. The LNB has amp so that they can amplify everything already there. Then when there's attenuation on the cables, the noise gets reduced same amount and snr stays the same. But if you don't amplify at the LNB, then the snr will decrease when you amplify later. Same applies to all signals. The first stage is always to most important. If you google cascaded noise figure calculation formulas, you can easily see that most noise is crated at the first amp, and _assuming_ the first amp power level is adequate, then the later items don't count almost nothing. If the first amp is not enough, then all the filters and cables add plenty of noise.
So if that same applies to cameras, then the earlier you amplify, the better it will be for the end result.