Aggression can be, so I'd think that could lead to violence. That said, I'd argue that violent behaviour could be more a reflection of the self-restraint that already existed regardless of the PTSD. Meaning I don't think someone would become violent due to PTSD unless there was already the potential for violence there.

I think it also boils down to the circumstances around the violence though. Whether they were the instigator, or whether they were reacting to something that triggered their PTSD.

For example, one time when I was out with a group, one of the group members initiated completely inappropriate and unwelcome physical contact that triggered my PTSD. I grabbed them and shoved them away rather harshly, and I'm sure it shocked them quite a bit. They weren't hurt or anything, but there were other ways I could have handled that situation. It was an instant fight or flight reaction, I never even thought about it. I just reacted.

That's a lot different than feeling aggressive and seeking to violently take it out on someone though.