Jengo and Logan both chased or chase prey. Both are a bit awkward, loud and reactive. Sparkle, on the other hand, is much more stealthy, focused and patient. I did see Jengo nail a mouse once. Neither Logan nor Sparkle have nailed one while here with us... yet.
My biggest concern would be them getting injured during an attack. A squirrel biting them. A raccoon could be really bad. We also have wild coyotes not far. All that said... the head wants what the head wants. No idea how to stop that.