Blood poisoning? yes with proper care. It is a very dangerous bacterial infection, usually caused by a wound small or large that gets infected.
Now if you are talking about a poisonous substance in the blood like arsenic and other deadly chemicals, ingested or injected, then that would be subject to, how long or the duration of the poisoning.... and what substance was used. Chemicals effect different parts of the human body when ingested..... shuts down systems and can lead to death.
If it's in their blood, I'd say that recovery would be very difficult. When it's in the blood, it gets a free and fast ride to all of your organs. When it gets to your organs, usually thats when it gets fatal. You'd need to seek medical attention VERY fast.
Also you have to look at the long term effects to your liver, I am sure Katie would know more about this, but it is the bodies defense against poisons in the blood.