This work investigates global convergence properties of a safeguarded augmented Lagrangian method applied to nonlinear programming problems, with an emphasis on the role of constraint qualifications in ensuring boundedness of the Lagrange multiplier estimates, also known as dual sequences. When functions with locally Lipschitz continuous derivatives define the constraint set, we prove that the Error Bound Constraint Qualification is the weakest constraint qualification that guarantees boundedness of the dual sequences generated by the method. The condition is also known as the local error bound property, metric subregularity, or calmness constraint qualification. We further show its equivalence to a Polyak-Łojasiewicz inequality for the quadratic infeasibility measure, which in turn is equivalent to the recently introduced relaxed quasinormality constraint qualification. Moreover, we prove the feasibility of accumulation points of primal sequences generated by the augmented Lagrangian method under a Polyak-Łojasiewicz inequality for the quadratic infeasibility measure. Our results provide a sound primal-dual global convergence result under a weak and well-known condition, reinforcing the effectiveness of safeguarded augmented Lagrangian methods over non-safeguarded approaches.