Ocelots, the stray cat's spiritual predecessor, hunted down chickens when not tamed (and still do). However, this trait was not carried over to stray cats, who only scare away phantoms, another bird-like mob.
While ocelots also attacked baby turtles, I don't think cats attacking turtle is a good idea, especially if there are turtle eggs near the village the stray cat spawned in.
- Summon a chicken
- Summon a cat
→ Notice the cat doesn't attack the chicken