Yes, poverty and crime do correlate strongly. Although be careful about conflating violent crime and property crime with each other.

That said, correlation is not causation. There is likely /some/ causative element between poverty and crime, but it is not absolute, rather poverty is also strongly correlated with other non-criminal behaviors that both lead to poverty and lead to crime. There is definitely a cultural element in wealthy countries to generational poverty, just as there is a cultural element to criminality.

If we can break that cycle for people, it benefits society as a whole, and I think it's worth investing what we can as a society into doing so, however current research certainly doesn't support deferment of responsibility for criminality because of poverty.