There isn't any good data to support or refute that, but the correct pronoun for a transgender woman is she/her unless she says otherwise. The US federal government has commissioned a study to examine a link between gender dysphoria, transgender identity, and violence, but even before it's begun there are serious questions about it's methods that would likely prevent it from being peer reviewed or replicated which would make it worthless scientifically.

I saw in other comments you were meaning that allowing a transfem prison to either transition or continue their already in progress efforts, but no one could say with any authority how that would effect levels of violence. In US prisons violence is an intentional feature rather than something the powers that be would prefer to mitigate. Threats of physical and sexual violence and their application serve the interests of the prison industrial complex which seeks to punish criminals and deter would be ones.

The US employs punitive justice and the suffering of those who are incarcerated is the point. Denying transgender prisons the ability to maintain their transition serves that goal, but also is a relatively safe way of stripping rights away from transgender individuals in a way that can seem unsavory to defend for a large portion of the US population which serves authoritarian political interests.

That's what they did to Alan Turing for being gay. He killed himself.

Forcibly induced gender dysphoria is unlikely to make someone less violent

Potenttially but not everyone is in prison for violent crime and I'm not sure who wants to live in a place where something like that is forced upon people.

Don't force anyone of course

With these things, you cannot deal in certainties. So the best answer is probably there is a high likelihood that a theoretical, voluntary transition like that would lower aggressiveness. However, and I assume the down votes are a reflection of that, there probably is a way to achieve that outcome, including medical procedures, that doesn't require a transition. And since that's unfortunately a hot button issue, linking a gender transition to a form of criminal punishment is not a good look.

Physical integrity is a highly valued right even in countries that still do capital punishment. So few people would put your theoretical plan here into a therapy plan or the law. A transition should be a personal decision based on an inherent need of the self and not an item on a menu of therapies that might get you out of the institution faster.

There are no stupid questions (well, hardly any) here but there are ones worded off the cuff that may lead to a pile on. I'm afraid yours here falls into the latter category.

Bradley/Chelsea Manning did it to himself while in prison, but wasn't known as violent before or after.