Its a wellknown phenomenon with leds. Laser diodes arent likely to behave much different, but this all happens -below- the lasing treshold.
The cause lies in semiconductor impurity. This causes small areas of the active area to have different bandgaps from the bulk of the diode, and those produce some light when driven at a voltage below the treshold for the bulk.
These emissions are still present when driving the diode at full current, but are then overwhelmed by the bulk color. No population inversion is achieved though, so they are pretty much useless for laser construction. Compare it to the difference in a HeNe laser between its output color and what the gas mixture emits: The emission is fairly broad, but only a few wavelengths can lase in those tubes.