Do you see a light when the LED diode in the reverse bias?

Not usually, unless you mean a LED. It depends of the kind of diodes. LEDs will emit light but not most regular diodes, though some may produce infrared light.

In the case of LEDs, the answer is yes. When an electron crosses the PN junction and falls into a hole, it emits a photon. The frequency depends on the energy, which is determined by the forward bias voltage. That is why a red LED requires more voltage than an IR LED, and less than a green LED.

So a regular diode with a forward drop of about 0.7V is emitting infrared (IR) light. However, most of the photons are reabsorbed in the semiconductor body or stopped by an opaque case. An LED is a special diode doped for a higher voltage and constructed to let as many of the photons out as possible, set in a reflector and usually with a lens cast into the plastic case.

There are a few glass-cased diodes which emit a deep red light, that I observed in a few audio amps. They drop more than the typical silicon diode's 0.7V. But overall, you typically cannot see the light emitted in a rectifier diode due to the absorption of the case and the semiconductor itself, and the fact that it is usually infrared.

You might try some experiments yourself by removing the IR blocking filter that is normally installed in webcams, or find an IR sensitive security camera. All CCDs (the light sensing element in a video camera, digital camera, or webcam) are sensitive to infrared, but most have had a filter added to block IR so as not to spoil your photos. Then get some glass cased silicon diodes, point contact will have more viewing space, and a 9V battery and a 220 ohm resistor to put in series to limit the current. This will give you about 36mA through the diode.

Then point the camera at it and turn out the lights or put it in a light-tight box and look for a glow from the diode.