If Homer gives me a feasible result for the given configuration with a system life time of 20 years, can I be certain that the battery will survive these 4 years?

Certainly not.  Even under carefully controlled conditions (controlled temperature, regular cycles of a fixed depth, fastidious maintenance) it is difficult to predict battery lifetime.  Real battery banks are subjected to all kinds of temperature and operational stresses that affect performance and lifetime in complex ways.  Battery banks are mysterious and difficult to model accurately.  Our approach with HOMER is to keep things simple and transparent.