No, not necessarily.
It's true that growing up that way normalizes violence for some, maybe even most. The statustics are clear that most abusers were abused themselves. That's why we say that "hurt" people hurt people.
But.
That's not a given and it's also clearly not always the case. There are plenty who grew up in dysfunctional and abusive homes who DON'T become abusers. They tend to become protectors instead. They do what they need to do to spare their own fsmilies that same fate. They change the pattern. It's their primary focus their whole lives.
We know how many abusers were abused, roughly. What we don't seem to have a handle on is how many abused become abusers and how turn away from violence.