In this paper, we present a theoretical analysis of augmented Lagrangian (AL) methods applied to mathematical programs with complementarity constraints (MPCCs). Our focus is on a variant that reformulates the complementarity constraints using slack variables, where these constraints are handled directly in the subproblems rather than being penalized. We introduce specialized constraint qualifications (CQs) of the quasi-normality type and establish a global convergence result under these assumptions. In addition, we analyze the behavior of the associated dual sequences and prove their boundedness under the CQs introduced. These conditions also yield a new, simple, tailored error bound property. Finally, we compare this approach with the standard AL framework in terms of theoretical properties and numerical stability on problems from the MacMPEC collection. Our results indicate that maintaining complementarities within the subproblems leads to improved numerical stability.