yes it does...read about penalty method and lagrange multiplier method to enforce constraints in non-linear optimization problems...you'll get the idea
It affects the load-displacement curve only if your interface is subjected to compressive forces. The penalty stiffness has to be introduced to avoid penetration during compression.
The traction-separation relationship was implemented by Camanho et al. in Abaqus. Rgarding his description, Kp= Tn/(1-d)*Delta(n) o rKp= Tt/(1-d)*Delta(t) where,
Kp: Penalty Stifness
Tn, Tt: the normal and tangential cohesive tractions
d: scalar damage
as the damge scalar d goes to zero so when there is no damage you have high penalty stifness so which means load increase in load-displacment curve and visa-versa when damage is high.