If the economy is not always on the Price setting curve, can the Central Bank target unemployment? In the usual textbook model, in which there's imperfect competition, the economy is always on the Price-Setting(PS) curve, and to have a target unemployment level, above equilibrium unemployment, will cause an inflation bias. 

First, is it possible for the economy to be on the wage-setting curve every time, but only in the PS curve in the medium-run? In this setting, would there be some leeway for a central bank to target also an unemployment level different from the equilibrium one, instead of just inflation, without causing inflation bias?

Any help would be appreciated.
The role of the central bank is solely to enact monetary policy, not government (fiscal) policy. Monetary policy of the central bank is independent (in the legal and political sense) from government.