I don't know about negative points, but I have a feeling it would either go straight to the shredder or not even be looked at.

If they don't ask for it, don't do it. It's pretty simple. Remember, your app is screened by a computer and an HR company first. They are sifting through thousands of applicants. You will get the call if your app meets whatever wickets they've set up. It is not like a corporate gig where a chief pilot is manually scoring each app.