Yeah, it does apply to damage taken rather than wounds suffered.
Shield drones and saviour protocols can make things funky though, so it's worth taking a look at this using examples.
A shield drone is shot by a lascannon and fails its invulnerable save. The opponent then rolls a D6 for damage, and inflicts four damage on the shield drone. The drone must then make FOUR feel no pain saves to survive, one for each point of damage.
A crisis suit is shot by a lascannon and is successfully wounded. You use saviour protocols to transfer this to a nearby shield drone. This is done before making any saves or rolling for damage, as specified by the saviour protocols rule. Now, when using saviour protocols, the shield drone does not take the damage that the crisis suit would have suffered but instead suffers a single mortal wound. This will only inflict one damage, and as such, the shield drone only needs to make a single FNP save.
So yeah, it's one FNP save per point of damage taken, just make sure you remember how much damage the unit is actually taking.
Hope that helps