True.
On the other hand, the death penalty removes souls from the pool of those that may be saved to spend eternity with God - something He wants of even the vilest sinners. Jonah found that out when he decided that those in Nineveh were too evil to deserve being saved and God insisted that he go....
The death penalty is not instant. Before the death penalty is carried out, there is plenty of time for the condemned to realize the truth. In the Bible, the thief on the cross was saved during his execution.