Can I connect the 16200B to a 4-terminal pair instrument by using the 16085B adapter?

No, basically, the 16200B cannot be used with a 4-terminal pair LCR Meters and Impedance Analyzers. It is because the Low side of bridge circuit is shorted to ground by the current flow path through the outer conductor of 7 mm coaxial connector and the outer shielding conductor of DC source Input (BNC) connector when an external DC bias source is connected to the 16200B.