I have a level 11 mix build power armor inquisitor and have unlocked and with items got to level 10 of the toughness perk points. The box which highlights the 30+ regen bonus, lights up, but is not showing up on the charactersheet, nor does its effect take place during a mission. 

However, if I take the points out of that ability and place it into warfare, it does adjust the character sheet and the effect is in mission as well.