Josie, I am not an attorney, but I am a verified health professional (advanced practice nurse anesthetist) and can answer this.
At the present time, it's my understanding that executed U.S. prisoners cannot be post mortem organ donors because their manner of death is officially a homicide/ judicial death. That means they are released to the medical examiner upon death. To my knowledge the cadaver cannot be harvested for skin, bone, or corneas-- which typically can be harvested many hours after death.
I am not certain about living donation. If a death row prisoner were to demonstrate that they were a perfect match for a blood relative for a life saving bone marrow/ blood/ tissue/ kidney/ partial liver transplant, AND they wanted to donate, AND there was not another donor available that was as good or a better match, I think attorneys could make a compelling case to allow the condemned prisoner to be a living donor.
Electrocution is also judicial homicide. As well as rendering the body unsuitable for harvest.
There would be no circumstances I can envision where a U.S. condemned prisoner would be brought to an OR and harvested (heart, lungs, etc) as part of their execution process. For starters, they are not declared brain dead by statute, as they don't meet criteria for brain dead donation. There are SOO many medical, legal, and ethical issues, we could discuss this for months/ years on a thread and in a national discussion. I can never envision this happening in the U.S.
Physicians and nurses do not participate in the actual executions, except to declare death in some cases. Medical personnel do not prepare the equipment or medications used in executions, nor do they place the IVs-- even if the prisoner has "difficult access". All of the steps are performed by corrections personnel.
One issue that has been forefront in my professional literature for the past 3 years or so is the widespread lack of availability of sodium pentothal, which is part of the "3 drug" execution process in most states (along with succinylcholine or pavulon to cause skeletal muscle paralysis, and potassium chloride to stop the heart.). Pentothal is a very old drug that only had very limited use medically (mostly in anesthesia) until a few years ago. The few companies who were producing it have stopped. The current "stock" of pentothal nationwide is expiring/ expired, with no new company stepping up to produce it. (The dominant use now is executions, and that is sort of controversial and bad for retail business!) Other drugs cannot be substituted in the execution process without being put thru the legislative process, which has caused some states to put executions on hold while they re-write (and deal with the politics) of changing the lethal injection cocktail in their state.
http://abcnews.go.com/Politics/deat...ion-drug-short/story?id=11668456#.UX1V_SMo7fk