Does my electric clearing field actually make ions?
The circuit ground is just a reference point for measuring voltages in the circuit. 

The clearing field is generated by the difference of electric potential (i.e. voltage) across the plates of the "capacitor", therefore the field configuration inside the chamber is not influenced by the actual potential of the ground node.

Of course this assumes that the chamber is well shielded/insulated and there is no other path (other than the one through that generator, that is) that charges may follow to reach ground. 

Note that when you are saying that your ground node is at some voltage other than 0V (ground is at 0V by definition) you are implying there is another reference in the system with respect to which your ground node has a different potential. You should examine your overall system and ask yourself if this other reference point (some other object, e.g. the earthing ground of your electrical system) might interact with your chamber and if there is a low impedance path from that "new" reference to your chamber that might allow charges to follow a different route.