In certain situations, sure. She's a hunting dog and loves it.
Birds - absolutely. I dislike birds, and they always take off, which makes it not-so-likely she'll catch one. I actually encourage it at the barn; we have some sparrows trying to settle in, and if she wants to chase them off, bless her.
Squirrels/chimpmunks/etc - it depends on where we are. If it is an area where they are able to get up a tree quick and aren't going to lure her into the road (ie if we are in the woods) I let her.
Cats - nope. We play "find the kitty" at the barn, where she hunts them down in the haybales, but they are always out of reach. While I don't ever intend to have cats, I don't want to encourage a behavior that would impact her welcome in other people's homes.
Horses are absolutely off-limits because she spends the day on the farm. Deer, she has no interest in chasing.