If they can get to a bird they will take the advantage of the 'free meal'. They are not normally a predator that will work hard for a chicken dinner the first time, but once they get a taste they will keep at it.
I agree with woodmort. Skunks are blamed for alot of the situations other predators do. Skunks are a very slow animal this doesnt mean they cant run it means there slow and pokey. I believe as a friend told me skunks are blamed for alot of the racoons stuff as a racoon is quick and witty its gone at the first trace of movment yet the skunk lingers trying to eat the left overs and is caught in the ""Act"" they are very Opportunistic, But I notice here on the farm they dont bother to much exept the trash pit.
I have a resident skunk around the garden. I've never seen him but I can smell him in the morning. Never bothered the chickens or anything else so he can wander at night in the garden and eat bugs and frogs.
Live and let live...my coop is secure.
The only problem I've ever had with a skunk was when I had a female duck that insisted on nesting in a pit in front of the chicken coop--first lost all her eggs then something killed her--although the latter may well have been a coon. Skunks can move fast, they just choose not to as there aren't too many animals that will challenge them--that may be why they appear dead on the road so often.