YES, one rotten apple can spoil the bunch, due to the release of ethylene.
The fruits themselves are producers of ethylene which is a ripening
Fruits will remain fresh and firm until the concentration of
ethylene surrounding them becomes high enough to stimulate further
Many fruits are shipped when they are not fully ripe and
then sprayed with ethylene gas on arrival.
From the Botanical Society of America:
In general, plant tissues communicate using classes of compounds
These are defined as substances produced in one
location that have an effect on target cells in a non-adjacent
In plants, germination, growth, development, reproduction,
and environmental response are all coordinated through hormones.
Although most of the main plant hormones are transported in the
vascular system of the plant, one class of hormones is transferred in
gaseous phase. This class includes the plant hormone ethylene.
Ethylene promotes fruit ripening.
Apple growers take advantage of this by picking fruit when it is not ripe, holding it in enclosed conditions without ethylene, and exposing it to ethylene right before taking it to market.
This process is why we have newly ripened apples grown in temperate North America even in the spring and summer (apples ripen in the fall).
From the British Columbia Ministry of Agriculture:
Ethylene is considered to be a plant hormone, a growth
regulator ... It
has sometimes been called the death hormone, because it promotes the
aging and ripening of many fruits and flowers.
Ethylene evolves naturally from plant
materials that are aging, ripening or rotting.
From NEWTON, Ask a Scientist:
The goal of a fruit is to spread its seed, so it needs to rot in order
to get the seeds out of the fruit. There are actually hormones,
especially ethylene oxide that promote fruit ripening.
If you want to
get a piece of fruit to ripen, put it in a bag with an apple which
generates a lot of ethylene oxide.