A long time ago I put a finch in with my green iguana, for just a shot bit. Even then I figured it wasn't the best idea, and when it fluttered the grown ig instantly jumped up and caught it. Finch DOA.
Some people have reported that their igs eat live mice, even though in nature they don't eat animals or insects (we think). We don't doubt their stories, and figure captive igs may have unnatural food cravings.