Only if he gets the pain token since pain tokens grant benefits to every member of a squad with the Power from Pain rule. If he rolls +1 Strength or the like however, no they do not get that bonus. They would need combat drugs of their own.
Also just because he has his special rule that benefits warriors/trueborn doesn't mean he must start with them (though he does if you want that benefit) nor does he need to stay with them. Once the game starts he can leave the warrior/trueborn squad he's with and join a melee unit if you like and the warrior/trueborn squad will keep their upgraded weapons.