I don't think it works that way. Crime or violence transference, if you will? Do you have any evidence that people that are violent get involved in drug crime?
Criminals* do not think
"I want to traffic drugs." as a first step. Criminals think
"I want to make a lot of money. What crime do I have to do to make a lot of money?"
Some criminals are violent. They will gravitate to the most profitable form of crime. Their violence will push out the non-violent criminals to other, less profitable forms of crime.
Since drugs are one of the most profitable forms of crime, it gets a lot of the violent criminals. Take away the drug crime opportunities, and they will turn to other forms of crime.
There are millions, if not billions, of men that beat up on women across the globe. Surely, they are violent men. I doubt that most are involved in other violent crime.
They are not the type of violent people I am talking about. I am talking strictly about career criminals who do crime for financial gain.
* When I say criminals, I am talking about career criminals. People who commit crime for income.