Most stat-mech techniques assume equilibrium -- so if a system isn't in equilibrium, then those results will most likely be incorrect.
Separately there are many people who try and solve systems outside of equilibrium, since the methods they employ don't require equilibrium they can be applied to non-equilibrium systems.
Indeed. The foundations of statistical mechanics do not assume equilibrium, otherwise you could not even develop a theory for equilibrium. Simply formulating what equilibrium is supposed to mean requires one to consider general non-equilibrium states.