I'm going to start by answering the question: No.
I understand the motivation behind the movement, I really do. It's a human, visceral reaction to an abhorrent crime that should never happen, even more so when the victim of said crime is
a child. It's hard to control that reaction. We don't want to think of a defenseless child ever enduring such a horrible experience (which more often than not is perpetrated on them by someone they're supposed to be able to trust).
I disagree with the movement for one reason: if a rapist knows that the penalty is execution, what will stop them from just going the extra step and killing the victim? Murder the victim and there's a window of opportunity for escape from being caught and convicted; if your victim is dead they can't point the finger, can they?
I've heard the term "soul murder" applied to those who are victim of violent crimes, and certainly rape is violent, even in cases where there is no physical abuse. You don't need to be bruised and bleeding in order to be traumatized. It's something that does kill a part of the victim, usually their innocence, their hope, or their sense of self-worth.
And I say no because I am a victim of repeated acts of rape. My mother's husband began sexually abusing me when I was 13 and had begun developing the body of a woman (making him an
ephebophile; he'd already begun abusing me in other ways before I was a "woman grown"). Certainly there was the risk of him being caught, which he eventually was, but he didn't fear for his life and in turn, I didn't need to fear for mine.
Can you imagine being in that situation and knowing that the person raping you could just as easily kill you? It's a terrible situation, certainly, but I'd much rather be alive and able to heal than dead and unable to do anything at all. And of course my family and friends would have had to mourn me instead of being able to surround me and support me, able to enjoy the rest of my life with them.
Do I think punishments for rapists (child rapists and otherwise) should be harsher? Sure. I think the Sex Offender Registry is a joke: if these people need to be monitored after they're released from prison to prevent recidivism, they shouldn't be released in the first place. Some can be rehabilitated and become productive members of society, and if they re-offend they can just as easily be tracked by their criminal record through police databases. The convicts that can't be rehabilitated, however, should remain imprisoned until they die.
A knee-jerk reaction to an awful crime doesn't do the victim any good.