Do insects respond to the detection of dead insects?
Yes, it is a common behaviour and is called necromone signaling (Yao et al 2009, see references in paper for many examples), and is probably used to avoid predators, parasites and disease. The chemicals used are often similar (unsaturated fatty acids), and seem to have an old evolutionary history (~400 million years). Many groups of species can also detect infected, not yet dead, conspecifics. Removal of dead individual is also common in e.g. ants (necrophoric behavior).

The paper referred to earlier (beside reviewing earlier evidence) also provides experiments of detection/avoidence in isopods and Tent
caterpillars (Malacosoma americanum), where they show avoidance based on crushed conspecifics, unsaturated fatty acids and (for isopods) intact corpses. 

Naturally, the same type of compounds are used by e.g. species of carrion beetles (Silphidae) to find their animal hosts, but then for the purpose of reproduction.