In this paper, we analyze augmented Lagrangian (AL) methods for mathematical programs with complementarity constraints (MPCCs), with emphasis on a variant that reformulates the complementarity constraints by slack variables and preserves them explicitly in the subproblems instead of penalizing them. Motivated by recent developments in nonlinear programming, we study quasi-normality-type constraint qualifications tailored to this framework, including a new relaxed quasi-normality condition. We show that these conditions are valid constraint qualifications for M-stationarity and establish that they guarantee the boundedness of the multiplier sequences generated by the AL method. Finally, we compare this specialized AL framework with the standard augmented Lagrangian approach on problems from the MacMPEC collection. The numerical results indicate that preserving complementarity constraints in the subproblems leads to improved numerical stability.