I think most of the time it is about how you have been raised. If mom and dad told you no and you had consequences for your actions then saying yes to drugs or alcohol might not be as easy as it is for those who had no punishment or real parenting. There are people who have addictive personalities but this is caused by underlying problems and anyone can be prone to this. So with the question; it could be nature or nurture.
I remember a campaign in the UK few years ago. On the backs of magazines they displayed an image of a baby sat next to a tiny rock of crack cocaine. Underneath it said "this is enough crack cocaine to get a new-born baby addicted for the rest of it's life." As to how this affects the baby physically and mentally, here's some info from drugrehab.co.uk: "Babies exposed to cocaine experience painful and life threatening withdrawal, are irritable, have poor ability to regulate their own body temperature and blood sugar and are at increased risk of having seizures." and: "Effects of Crack on the Foetus: seizures or strokes cerebral palsy mental retardation vision and hearing impairments urinary tract abnormalities autism and learning disabilities"