I have my doubts that it will work, or at least that it would work here (in Canada). When I was in high school I knew too many people who were smoking illegally for me to think that you could just slowly creep the law up the age groups and not end up with a thriving black market. Hopefully I will be proven wrong though!
To describe why I think this is unlikely to work in another way, I think banning it for young people is really only effective because they have almost no money, and the illegal sales to supply them mostly aren't done through criminal gangs using it to fund terrible things, but slightly older people who are just using it to earn a little extra money. Both of those break down once you start banning it for older people, even if it's always been illegal for them.
What should be banned and made illegal is the method Big Tobacco uses to process tobacco into such a lethal product [1]. If we banned this process, but permitted manufacture, sale and consumption of smoking products containing only unadulterated natural (i.e. no additives except water) tobacco, within 10-20 years, the mortality rates of smokers would plummet and return to what they were prior to the chemical revolution of the 1950s, which is probably far less though we don't know by how much because the studies only appeared after the chemical revolution.