Duterte promised to eliminate drug use in 6 months, Trump promised to build a wall on the Mexican border, all shockvalue promises to make yourself more likeable to the public. To be honest he could probably get rid of drug use in 6 weeks, but it would be a most ugly show to watch. If he can fulfill his promise in more time but with less violence it's always the better option, but I fear that's just not his thing.
No matter how much violence he use, it is not possible to wipe-out the drug trade. There are millions of drug users there, and as long as the demand exists, supply will also be there. If violence is used, then there will be a lot of collateral damage as well.
Yea, he can decrease the use in general, but mostly he'll succeed in skyrocketing the price of drugs. This will eventually make the business so lucrative that many people won't care for the dangers and there will always be someone supplying some amounts of drugs in hopes of getting rich quickly.