See "Licit and Illicit Drugs", by the Editors of the Consumer's Union, an extremely well-sourced, and well-regarded academic resource. Without federal prodding, there would probably never have been state laws regarding marijuana--it was too far below the radar for anyone to be interested before the feds started looking for new crimes to invent.
Phohibition of possession wouldn't have been practical, since hemp was still commonly grown as a commodity crop. I shouldn't think it unreasonable to assume that there were some successful prosecutions and incarcerations for violations of those laws.
Medical marijuana was regarded as about the same as aspirin is now, until the mid 1920's. The really astonishing thing about this period, is that it required an amendment to the Constitution to ban alcohol, whose detrimental nature is plain, whereas to ban marijuana, all Anslinger had to do was make up a bunch of racist stories about how you "cain't stop them spics and nigras from raping white women while hyped up on Marijuana with a 45". And tell these stories to a Senate committee, which later reported these stories, and NOT the AMA's strong objections, to the full Senate before the vote. The transcript of these hearings is about the most unshamefully racist document to be produced by our government in the 20th century. The war on marijuana started with deeply fraudulant testimony, and has been maintained by fraudulant testimony ever since.
The deceptions started before the first testimony was even heard. Why name the bill the "Marijuana Tax Act" at a time when very few people had ever heard the term, but virtually everyone knew what "hemp" or "cannabis" were? If you want people to know what you're talking about, you refer to it by terms they are familiar with. The only reason to adopt terminology they are unfamiliar with to refer to something they are familiar with is if you have something to hide.