Metal acetylides (MCCH, M = Cu, Ag, Au) were already experimentally detected in molecular form. Herein, we investigate the possibility of noble gas (Ng) insertion within the C-H bond of MCCH and their stability is compared with those of the reported MNgCCH and HCCNgH molecules. Our coupled-cluster-level computations show that MCCNgH (Ng = Kr, Xe, Rn) systems are local minima on the corresponding potential energy surfaces, whereas their lighter analogues do not remain in the chemically bound form. Further, their stability is analyzed with respect to all possible dissociation channels. The most favorable dissociation channel leads to the formation of free Ng and MCCH. However, there exists a high free energy barrier (29.3-46.9 kcal/mol) to hinder the dissociation. The other competitive processes against their stability include two-body and three-body neutral dissociation channels, MCCNgH -> MCC + NgH and MCCNgH -> MCC + Ng + H, respectively, which are slightly exergonic in nature at 298 K for Ng = Kr, Xe and M = Cu, Ag, and for AuCCKrH. However, the Xe analogues for Cu and Ag and AuCCKrH would be viable at a lower temperature. AuCCNgH (Ng = Kr-Rn) molecules are the best candidates for experimental realization, since they have higher dissociation energy values and higher kinetic protection in the case of feasible dissociation channels compared to the Cu and Ag systems. A detailed bonding analysis indicates that the Ng-H bonds are genuine covalent bonds and there is also a substantial covalent character in Ng-C contacts of these molecules. Moreover, the possibility of insertion of two Xe atoms in AuCCH resulting in AuXeCCXeH and the stability of XeAuXeCCXeH are also tested herein.