This work examines the reliability of the Self Consistent Charge Density Functional based Tight Binding (SCC-DFTB) scheme to derive geometrical and thermochemistry observables for complexes and clusters made of Ag, C and H atoms. In addition to the currently available DFTB parameterization DFTBhyb, it proposes a new SCC-DFTB parameterization based on DFT Slater Koster integrals and recalibrated on atomic pairs MRCI calculations for clusters made of Ag, C and H atoms. Two sets of parameters were determined, one for restricted open shell SCC-DFTB, the other for spin-polarized SCC-DFTB. These two new sets of parameters, namely DFTB$^γ$ and DFTB$^{γpol}$ respectively, along with DFTB$^{hyb}$ , are first tested on Ag$_n$, Ag$_n$C and Ag$_n$H clusters. A key issue being the transferability of such parameters on different types of Ag-X bonds, the three sets of parameters are then tested on Ag$_m$C$_n$H$_p$ (m=1-3, n=2, p=0-2) complexes involving covalent and π metal-ligand bonds. The particular case of naphthalene C$_{10}$H$_8$ as a πligand is also investigated. In general, with respect to DFTB$^{hyb}$ results, using DFTB$^γ$ parameters leads to an improvement of geometries and energetics. In the case of Ag$_n$C$_{10}$H$_8$ clusters, the role of dispersion is evidenced. However, in a few cases, the geometries may distort due to a questionable description of charge transfer with DFTB$^γ$ and DFTB$^{γpol}$. The spin-polarized version of SCC-DFTB is suited to correctly describe open-shell species with more than one unpaired electron in their ground electronic state but is shown not to improve the results otherwise.