Let's take a moment here and assume that some person has been wrongfully convicted of a crime for which said person will receive the death sentence. Already, without your proposal, said person is being removed of the life, liberty, and pursuit of happiness promised to all American citizens, (or whatever values your country of origin guarantees for its citizens), and that is something utterly terrible, and to be stopped at all costs, which is why, until the very day that person is given a lethal injection, the courts go through appeal after appeal trying to clear this person's name.
Now, with your proposal, said person, once convicted, would be at the mercy of experimenting scientists until the day that they either received a lethal injection OR THE DAY THEY WERE EXONERATED OF THAT CRIME.
In any case, whatever reparations governments have to pay to the wrongfully accused would be drastically increased after such experiments were conducted. If there were some guarantee that the inmates were, indeed, guilty of the crimes for which they were sentenced to death, this might be a different argument, but as it is, until the day the Death Row inmate dies, they can be exonerated (and in some cases, even after that day).
In the real world, this proposal is unethical, and if you will not be swayed by the mutable standards of ethics, perhaps the standards of cost efficacy will do what morality cannot (I know for a fact most governments are trying to cut back on spending, not increase it exponentially).