Can children learn addiction from their parents?

Absolutely. Chilldren learn by modeling the behavior of those around them. Living with parents whom are addicted; this is what they see and know. They see how their parents cope with life, deal with feelings and deal with others, which are all usually dysfunctional in someone with an addiction. There is also a genetic component to addiction as well. These children may take on unhealthy roles, can't be "kids".
Probably. Addiction also has strong genetic factors which increase the "liking" effect of many activities. Seeing ones parents abusing increases the chance that the kids will imitate.