Don't think so. Simpson's paradox applies when you have two groups and independently rates of your variable are increasing within both, but the population of the lesser group is increasing faster. For example, if death rates for both whites and blacks were decreasing but blacks had a higher death rate, and the population of blacks was increasing, you would see overall death rates increasing. If death rates for both uneducated & college-educated white Americans were increasing but there were an increasing number of college-educated white Americans, you would see death rates decrease.

Neither of those seem to be the case here: it's just one group who, tragically, is killing themselves or self-medicating to death disturbingly frequently.