Interesting question, really... At first I immediately thought yes, as I would obviously grab the chance myself. But then another thought crossed my mind - why should they be allowed to just choose their own sentence? I'd understand appealing and asking the sentence to be lowered to death penalty, but that should be the decision of a court, not their own choice.

(Ah, first time for me to answer one of these, but the question was really interesting enough to make me do this.)