Where I live in N Texas it has become very invasive on my property. The birds love it & have helped it to reseed everywhere.

They may seed around some but are not considered invasive in the correct ecological sense (except for the Asian species in Alabama - the only state to declare any beautyberry invasive).

I won't mind if I get a bit of a clump in the area these are planted. They are on a berm between the road and the house and help obscure the view in both directions. If they get much further afield I will pull the strays. We used to have a hedge of Laurels in this spot and those were not only prone to become overgrown, but also seeded about in an obnoxious way. They have been gone for over 5 years and I still find the stray saplings hiding in the fringe of the forest. Beautyberry is also a much nicer looking plant.

Quite a few Old World origin plants from monsoonal climates have been able to spread from cultivation in the similar conditions of eastern North America. This phenomenon does not apply however to us here on the dry summer side of the continent on a routine basis. With kinds like Buddleja davidii and the large perennial knotweed species being if anything exceptions that prove the rule.

Had a beautyberry for years. Never saw a seedling.