He does drop his equipment but probably this early in the game is not a good time to try and farm it. That opportunity will come later.
I joined the Watchdog of Farron Covenant today and invaded a guy in the woods. But he had help. Still, I lasted longer that I thought I would. The woods are pretty much a PvP free for all.
Before proceeding any farther into the Farron Swamp I am going to return to the woods to fight the boss and then proceed in that direction. The inevitable boss in that direction is easier than the inevitable boss in the swamp.