I've personally seen fungus gnats burrow up under the bark of dead cuttings but it's hard to say if they killed the cutting or went after it after it died. Here are some college articles.
http://www.greenhouse.cornell.edu/pests/pdfs/insects/FG.pdf
The first few weeks of a crop are most critical for fungus gnat control. Larvae prefer to feed on fungi rather than healthy plant tissue. Although fungus gnat larvae can eat plant material, they need fungi in their diet for optimal survival, development, and reproduction.
Chewing by larvae can cause direct root damage, and provide an entry into the roots for fungal pathogens.
Seedlings and young plants without fully developed root systems are particularly susceptible to their damage. [Fig.3]
Unrooted cuttings are also particularly vulnerable, with larval feeding interfering with callus formation and thus root initiation. Adult fungus gnats do not cause direct damage to plants, but are considered a nuisance pest to consumers. In addition, adults and larvae have been implicated in the transmission of plant fungal diseases, including Thielaviopsis, Pythium, Verticillium, and Fusarium. Larvae may transmit fungal plant diseases via their excretion. Adults may transmit these diseases via excretion or by carrying spores of disease organisms on their bodies. Disease transmission by fungus gnats has been documented in lab studies, but it is not yet clear whether fungus gnats play an important role in disease transmission under commercial conditions.
http://extension.oregonstate.edu/gardening/do-your-potted-plants-have-fungus-gnats-0
Most fungus gnats are merely annoying and cause relatively little damage to plants. But several species of fungus gnat larvae feed on roots, causing damage to African violets and other houseplants. Others burrow into stems and leaves. Fungus gnat-damaged plants may show signs of wilting. Gnat damage may weaken plants and make them susceptible to root rots.
http://ipm.ucanr.edu/PMG/PESTNOTES/pn7448.html
Larvae, however, when present in large numbers, can damage roots and stunt plant growth, particularly in seedlings and young plants. Significant root damage and even plant death have been observed in interior plantscapes and in houseplants when high populations were associated with moist, organically-rich soil. Thus, a houseplant that is wilting may not indicate a lack of water, but rather root damage by fungus gnat larvae or (more commonly) other causes of unhealthy roots.