No Eddie was always himself with Venom. The same went for Parker when he was infected with Venom. It just allows them to act out of their own anger but they are still themselves. Eddie didn't want Parker to destroy the Venom since it gave him those powers so he got himself killed by jumping in with it on the pumpkin bomb.
I always was kinda confused about the ending of the movie, but I think that there were still traces of venom on Eddie, which was gonna blow Eddie up with it. I think that why Eddie told Peter, "Peter, what are you doing?" I think Eddie was a good guy, albeit angered.
The venom left his body to be an individual being when he was dying. It found him an unsuitable (pardon the pun) host when he was almost dead. So, it ripped itself off of him and slithered away. So, no he did not have venom when he was actually and officially dead.