If Iron Hands ex with Heavy Baton is KO'd by Quaquaval ex's "Exciting Dance" attack which pushes it to the Bench after doing damage, does Heavy Baton move energies attached to Iron Hands ex since it is on the bench by the time KO's are checked?

Yes. Heavy Baton checks for two things here: Iron Hands ex was damaged by an attack while it was your Active Pokemon, and Iron Hands ex was Knocked Out by that attack. So even though you don't check for a KO until the attack is completed, the criteria for using Heavy Baton has been met, so it can be used. This holds true for any similar Ability that triggers when the Pokemon is Active and gets damaged by an attack.

Relevant cards

SV2_52

SV5_151