I was wondering about the same thing. I got a leader only for the bonus to enemy skill, and my soldiers deal the same damage with or without the leader in the vicinity. So does anyone have any confirmation of this?
BTW how did you get 80% estimate? Is it 16% per each level above Average?
As to the OP's question about psionics' equipment, the ones I use seem to work. TrueShot vambraces show additional LongRange level when on. I noticed when they have the Protection Collar one, my soldiers have an icon showing that they have 1.3 bonus to Psi defense, and even 1.69 bonus when two psionics are around. But then again, they also have an icon when a leader is around, so who knows.
As for the Damage Collar, it does give a bonus damage - I tested it. Just need to test more if 2 collars give a multiplied effect. Hard to test in the battle, I tested that on the pillars of death - harmless and plenty of health to take
edit: I meant protection collar, not cloak one.