Dark Souls – How to Retrieve Loot After Pushing Knight Lautrec of Carim Off a Cliff in Dark Souls?

Yes you can indeed kill him, and you get 10 000 souls when you do. As far as being killed with arrows, unfortunately I could not get a clear answer. The consensus on the forums I've looked through seems to be that he'll get down to about half health, at which point he'll cover his head, seemingly healing himself. There have also been several glitches reported where he died randomly.

Here is a video of somebody accomplishing the task:

Yes, he eventually kills the Fire Keeper located near the Firelink Shrine. If this does end up happening, you can eventually bring her back to life (when you reach Anor Londo) by invading Lautrec's realm and retrieving her soul. It is inconvenient however, as you cannot interact with the Firelink Bonfire until you bring the Fire Keeper back to life.