It seems to be that Sleeping Tree Sap is based off the urban legend drink "Purple Drank" that is a purple concoction with vaguely narcotic effects, what do you think? Is this just a coincidence or is the similarity intentional?
probably a nod to the urban legend/myth since Bethesda LOVES to put in nods to everything from Pop Culture references to past games to other franchises (case in point being the Sweet Roll comment from the Bully game by R*, i think). so, yeah, it's entirely possible that it's a cleverly placed reference.
Urban legend? "Purple Drank" is a slang term for perscription cough syrup containing codeine, which, yes, is an opium-based narcotic. It's not a myth. As for Sleeping Tree sap being a reference to it, maybe? Blurred vision and a distorted sense of time are pretty common symptoms of just about anything. Hell, even alchohol can cause that.