I really don't see this as the most likely scenario. Why would it follow that legalization of a drug would lead to more addicts? Cigarettes are legal and addictive and I don't smoke them. Heroin and meth could be legal and I wouldn't do those either. Legal doesn't imply uncontrolled and unfettered access by all and I really just don't see a huge influx of hard drug users, the people who want to experiment with them already do so regardless of legality, health effects or cost.
Further, legalization and taxation should cover the additional medical costs, the price of each pack of cigarettes is currently about 56% tax revenue and distilled spirits are around 50%. Sin/vice taxes already fund dozens of other things besides adult health care costs, if anything I would expect them to be exploited as a revenue generating machine that politicians could gouge for cash since it's so easy to demonize.