I have heard of and have tried flyfishing for Carp using imitations of bread, dog biscuit etc (I used imitation 'maggot' fly, and sprayed loose maggot over the top), but have not heard of them coming to a lure worked as a small fish. I once played a carp for about half an hour that I had hooked fishing a tiny buzzer in my old favourite trout fishery. Lost it in the end unfortunately, but knew from the owners it was a twenty. You hear the odd report of Carp taking deadbaits intended for Pike I suppose, but you'd have thought that there would be a lot more caught that way if it was feasible. I used to spend a lot of time at smaller commercial type places and would fish a small livebait roach in the margins, intended for a big goat of a Perch, and never had a take from a carp. Maybe something to imitate very small nymphs, twitched really slow across the bottom?