I am wondering if I can put storage such as Pumped Hydro, CAES, etc. in a model?
HOMER cannot explicitly model pumped hydro or CAES. But if your system is all AC, you can model CAES and pumped hydro fairly well with the existing battery module. The battery has to go on the DC bus, but if your system is all AC you can specify a huge, free, and 100% efficient converter and then there is effectively no difference between AC and DC.
This approach will not capture the effect of discharging a CAES system through a combustion turbine and second order effects, like the change in head of a pumped hydro system, but it may help with conceptual analysis.