Is a pn-junction diode ever said to be "on" in reverse-biased conditions?
It depends on its history, and what you mean by 'on'.

Forward biasing a PN junction fills it with carriers.

When you apply a reverse current, the carriers get swept out. During that time, the diode is still conducting, and the voltage across the junction is low. Is it 'on' then?

This charge storage time limits the switching speed of junction diodes used as rectifiers. 

Eventually, the charge in the junction will be depleted, and the junction voltage will rise rapidly. This is certainly off. 

The turning off process happens very rapidly, and this feature is used in so called 'step recovery diodes', usually to interrupt a current flowing in an inductor, to generate a very sharp voltage transient.