Can elastic bands simulate gear?

I once heard a coach say that training with equipment improves your technique, because equipment teaches you to keep pushing against the weight. Thus implying – I suspect – than even raw powerlifters could benefit from training with gear.

Since equipment, generally speaking, accumulates elastic energy in the eccentric phase, which you can 'spend' in the concentric phase to lift the weight, one could assume a sort of equivalence with elastic bands (but not with chains). Think about elastic bands attached at the top of the power rack (also bands attached on the floor would give the same net effect, but you'd have to take off weight from the bar).
The big difference is, of course, that with equipment the Joules (units of energy) are stored on yourself, which implies compression on your muscles and joints, while with the bands the energy is stored externally.

But if one could calculate the exact amount of energy stored in a bench shirt (and I suspect the best way to do this would be to measure bar speed with and without the shirt) and replace it with an equivalent energy stored in the bands, would the two conditions be very much different?

I'm strictly raw so I can't say much about gear.

But from a theoretical standpoint the elastic bands and gear would probably produce different effects on horizontal motion of the bar. Deviating from a vertical path with the bands set up as you described would produce a corrective horizontal force that may or may not be helpful. The same might not happen with gear and you could wind up with a narrow effective range that forces you to do it right or not at all. So in one case you get more tolerance for errors and less in the other.

If that's true then the logical conclusion would be to use gear even as a raw powerlifter.

Not really.  Yes they make lifts harder at the end of the range of motion, where gear is less supportive.  If you are looking at it from a muscle standpoint, I guess.... but looking at it by the way it feels or the technique, then no.  Especially not for bench.  Deadlift I think to be the most similar bands versus suit but bands can't replicate the pressure feeling from the suit either

To answer your question from the other angle, I think training against light bands from time to time is an incredibly effective way to help you push through a whole range of motion.  It has helped me learn how to fight through the end on deadlifts and on bench