Yes and no...it's complicated.
While I don't think society Romanticises drug use per se, they do tend to treat it in a very naïve/stereotyped way that may have the unintended effect of romanticising drug use. For instance, in even in movies/television that don't engage in pulp fiction style glamourisation of drug use, drugs are still used as a symbolic shorthand for alienation, rebellion, living a high speed lifestyle- 'live fast, die young' etc etc. Only a certain type of character uses drugs and what drug they use will tend to tell you something about their character- high rolling masters of the universe only use/get addicted to cocaine, stressed suburbanites take pills (opiates or benzos) while crack is consumed exclusively by ghetto-dwelling gangbangers etc etc. Heroin probably has the most extensive/ingrained mythology associated with it- the post-WWII generation firmly established the 'dope fiend' archetype in both film & literature with The Man With the Golden Arm by Nelson Algren (made into a famous movie), Junkie by William S. Burroughs, Cain's Book by Alexander Trocchi and numerous others all contributing to that which is now known as 'Heroin Chic' thanks to the early '90s. This can lead to drug use, particularly use of particular drugs coming to be associated with certain archetypes/stereotypes...this can in turn lead to people who are drawn to these archetypes ending up being also drawn to drug use- like how grunge and heroin chic were separate things that happened around the same time, but which served to feed each other.
If you actually read/watch most works that 'romanticise' drug use they actually do nothing of the sort- William S. Burroughs, in my opinion, never wrote anything that was not derived from his experience of opiate addiction. 95% of it is completely accurate and not really that 'glamorous' (any epic high is always balanced by some suicidal low) and the 5% that isn't true can be seen as an illustration of the psychology of addiction, that even well educated & informed (to '50s standards) opiate users will tend to focus on the (questionable) fringe benefits of addiction. Even Pulp Fiction, which is more glamorous in its depiction of drug use than many similar movies, has a long graphic heroin OD as well as a bunch of young,
white dealers being casually murdered over a debt (if I remember correctly- haven't seen it in ages). That's not exactly romantic...even DeQuincy who talks about the 'morally improving' effects of opium intoxication writes at length about the horrors of addiction and his feelings of helplessness due to his inability to quit!
If you don't read/watch these things to the very end you could be forgiven for thinking they're encouraging drug use- but most of the time it ends badly. In most mainstream entertainment drug use is a 'bad guy' characteristic and the bad guys always lose...and the more thoughtful, intelligent works about drug use tends to feature descriptions of the negative consequences of drug use.
Now, here's the bit ugly BUT in my thoughts on this one...
But I do think that there is some relationship between the depictions of drug use, in both 'high brow' and 'mass', entertainment and drug use generally in society. To be honest, when I was a kid (like 10) I always knew that I was going to take drugs when I was older- why? Because the media told me that drug use (particularly heroin, as it goes) was associated with everything that I liked back when I was a kid. When I was around 12-13, at the age that I first started getting really into 'my' music- my music was punk rock. As it happens this was in the late '80s/early '90s, so the whole grunge thing was obviously first breaking and came to its height, peaking with Kurt Cobain killing himself. So grunge was in the media and because of that you also had a bit about the first wave of UK/US punk as well as a touch about US Hardcore (Flipper t-shirts worn by a certain junkie

)...and there was a strong connection between heroin and the music I liked.
I'm not saying that being involved in punk led me to develop a taste for opiates- not at all! My mother being prescribed codeine followed by dihydrocodeine followed by morphine (which I could get turned into heroin) had far more to do with it (yes I am a terrible person & I do feel guilty- but I was a kid & she never went without, I only took the excess!). And most of the coverage was extremely negative! Even before Kurt killed himself- there was a huge uproar after he overdosed (in Italy? Or Spain? I dinno) and there was an even bigger uproar when Courtney Love admitted to using heroin before she knew she was pregnant. But never the less it piqued my interest. I read Junkie, Queer & the Yage Letters by William S. Burroughs, I read Requiem for a Dream & Last Exit to Brooklyn by Herbert Selby Jr, I read Howl & America by Ginsberg, I read Cain's Book by Trocchi...once again, most of these are either negative, realistic and in Selby's case downright moralistic- but never the less it all served to 'prime' me with a deep seeded curiosity about opiates.
I'm not afraid to admit that I was young and dumb and impressionable as hell- I was so deeply unhappy living in my own skin that drugs seemed like a viable tool to treat my teenage existential angst. All my heroes said so- actually they didn't, but it seemed like at worst drug addiction had served as some sort of right of passage or baptism of fire that had transformed them into the people that I idolized. It's painfully naïve stuff- but the truth is that if you made a list of my 'top 10 role models/inspirations' at age 14 almost all of them would have either been, were or died as opiate addicts...and to deny that this had something to do with me deciding to take 300mg of codeine one night would be dishonest/stupid. A couple of years later I became more interested in psychedelics due to a broadening of my musical tastes which led to my first forays into the world of the drug trade as I tried to find someone to get some LSD off.
I'm not trying to absolve myself of any responsibility for my choices- even choices that I now consider to have been extremely naïve/stupid with the benefit of hindsight...but the fact remains that I always knew that I was going to use drugs 'when I grew up', I found a picture I drew of a 1%er bikie when I was 5 for fuck sake! (there was club house near where I lived) Why? Because I have always felt alienated from the 'mainstream' and attracted to whatever sort of 'counterculture' was on offer...and the media never failed to draw a close distinction between drug use and the counterculture. I always knew I was going to take drugs- what drugs I ended up being attracted to had far more to do with circumstances and personal taste despite my taste in entertainment/music playing a smaller role...but I always knew that I was going to take drugs and from a fairly young age I have always tended to gravitate towards drug users as I find that more often that not there does exist some commonality between people in the drug scene beyond a shared DOC. For whatever reason it's a certain type of person who uses drugs and different personalities are often drawn to different drugs- even just amongst the hardcore, dreadlocks & homemade clothing hippies there is a clear personality divide between the 'LSD over MDMA' kids and the 'MDMA over LSD' kids.
It's very complex. No matter how you depict it, the nature of drug use and particularly drug addiction means that any depiction will be romanticised by those who are already users of that drug. Like Requiem for a Dream- there is no way that you can say that that movie encourages drug use or drug dealing- anything positive is shown to be both temporary and illusionary...but that movie has a strong junkie fanbase. The same with Trainspotting. I suppose it's an anti-hero thing- that whole what they reject we embrace, what they discard is what we venerate thing that is the cornerstone of so many 'youth movements'. I think the media does a great job at accidently advertising/encouraging drug use. The medias approach to MDMA & raves is the best example- MDMA went from being a unknown niche drug to EVERYONE knowing how fantastic it was to dance all night on! BOOM! Rave culture, dance music going from underground as fuck to eclipsing corporate dance pop. Oops.
That was an epic TL;DR post! Sorry guys, I've been smoking this brain splittingly well grown Jack Herer- making me ramblerambleramble like a motherfucker....