Bad idea. If you know the cause of death, that's one thing. But a mysteriously dead fish could be a time bomb, you definitely don't want to feed that off.
It also depends heavily upon the immune system of the predatory animal. If it's a wild caught fish, and it's eaten live food its whole life, it's more likely to be able to fend off pathogens that it'd pick up from scavenging a dead fish. But if it's a captive bred pellet feeder, it's more susceptible to parasites and pathogens because its immune system is not as strong.
However, there are still some diseases that could possibly be transferred. It's your choice, given that information... but it's not a good idea.
That being said, when I have an invert that dies, I always feed it off. My pike cichlid got my last crayfish after it passed on, and my blue tongue skink has eaten a crayfish and a few breeder hissing cockroaches. Most (not all) diseases that may kill an invertebrate are unlikely to be able to attack a vertebrate, due to their biological differences.