Ultrafast ground state nuclear dynamics of small coinage metal clusters is theoretically explored in the framework of negative ion to neutral to positive ion (NeNePo) femtosecond pump-probe spectroscopy with the aim to determine the scope and perspective of this technique. This approach involves the preparation of an initial ensemble in the anionic ground state of the cluster, one-photon detachment by the pump pulse, the propagation of the system on the neutral electronic ground state, and detection via the cationic ground state by a time-delayed ionizing probe pulse. The calculations of the NeNePo-ZEKE signals under the condition of zero kinetic energy electrons are based on the combination of the Wigner distribution approach and ab initio molecular dynamics (MD) "on the fly" in the framework of gradient-corrected DFT for the propagation of an ensemble of classical trajectories and involves the average over the entire phase space. We have, chosen examples of Ag2Au and Au-4 to investigate time scales and the character of isomerization processes that are influenced by a local minimum corresponding to an energetically high-lying isomer with the structure related to the initial anionic structure. Capture of the nuclei within the local minimum takes place with dephased (Ag2Au) or nondephased (Au-4) vibrational relaxation. Structural relaxations leading to isomerization processes are in both cases of delocalized nature and take place after 1 ps. In contrast, the Ag-4 cluster represents an example for which isomerization processes do not occur, since rhombic structures with slightly different bond lengths are global minima of the anionic and neutral ground states. Therefore, the relaxation dynamics is characterized by regular oscillations, which serve as fingerprints of structural properties. On the basis of the analysis of pump-probe signals and underlying dynamics, this contribution provides information about conditions under which structural properties of gas-phase clusters (global and local minima) and isomerization processes can be observed in the framework of the NeNePo-ZEKE type of spectroscopy. The latter is important in the context of applicability of this technique to the investigation of cluster reactivity.