From my understanding the agonizer is a Dark Eldar weapon that disables or kills models by overwhelming their pain receptors. It usually takes the form of a whip but can be any number of other weapons made of an alloy of ghost steel and handwavium.
It seems that it inflicts minimal physical damage but basically shuts down the targets brain with an overload of pain.
Now the Feels No Pain special rule seems to indicate that model can "fight through fearsome wounds" because of force of will, bionic augmentation, foul sorcery, drugs or, presumably, some sort of mental illness.
So the intent would seem that the model has suffered some very painful but not necessarily crippling injury, like having a hand blown off, but struggles on because it can ignore the pain caused. Now the stat of Toughness takes this into account already to some degree, being combination of the models physical resistance to injury and its ability to ignore wounds, but this would seem to be an extra resilience to that on top of it.
Would you think that the agonizer is so potent that it even overcomes this to a large degree, allowing the normal additional save due to such a special rule or should the model receive a bonus to its feels no pain spacial rule?
The thinking for the latter would be that the model can ignore the pain from having a limb blown off but when it fails its save that represents an injury that ignoring the pain doesn't help, so if the leg is blown off the model still goes out of action because even if it doesn't succumb to the pain it either bleeds out or can't fight effectively any more.
So howling in frustration the model continues to crawl towards the enemy but we can ignore him for game purposes now.
If that is the case then I would think that the agonizer's effects on such a model would be negligible because it is capable of ignoring pain and the agonizer disables by causing pain.
I'm thinking about giving Feels No Pain models a +1 to their Feel No Pain roll against agonizers or similar weapons.