Yes, some people are more genetically disposed to withstand drug use. If Ozzy Osborne had his genome sequenced to better understand how he's still alive after years of hard drug and alcohol abuse, then this is proof. Some people are just more resistant to drugs - it's in their genes.
Different people are predisposed to be affected more or less by nearly anything, such as allergies to certain foods or even the ability to suggest milk. It definitely makes sense that different bodies withstand the long term effects of drugs and alcohol differently. Just sequencing Ozzy alone wouldn't help though. A lot of different people would have to be sequenced, including those killed by drug abuse.
Having a weak heart, or a bad liver, or diabetes are all things that make it harder for people to recover from using drugs or alcohol. It stands to reason that there are genetic reasons that he would be able to survive a history of drug and alcohol abuse. His habits for recovery also played a part for sure.
Certainly from anecdotal evidence I would say that some people are far more genetically predisposed to withstand the rigours of drug abuse whereas other people are equally genetically predisposed to being adversely effected by the same routine and substances. Sequencing of Mr Osborne's DNA should be very useful in proving or disproving this idea.