In the early 1970s, 'dope' among the young people I knew meant opiates; however, due to derision of authorities' claiming that marijuana were the equivalent of heroin, people started using 'dope' ironically (in the best-honed sense of that word, as well as in today's more usual sense of 'satirically'), as in 'Yes, Dad, I smoke a joint every couple of months, I'm a huge Dope Fiend.'.
I forget if it were mentioned in the segment, but 'doping' was the application of a substance to the fabric wings of the original æroplanes, so calling 'airplane glue' for model kits 'dope' were natural, and that cement's use to get high the subject of yet another overblown drugs-scare in the 1950s and '60s.
Somewhere, I'd guess in the book "For God, country, and Coca-Cola", I've read that in some places early imbibers of Atlantan Courage called it 'dope'; if true, that would place the 'drugs' sense of the word at or around the time of the first powered flight.
I've never heard anyone outside our family call it that, but we've called Hershey chocolate syrup "chocolate dope" since before WWII. To a lesser degree, we've used "dope" to refer to other sticky, high-poise liquids, including not only other ice cream toppings (but not pancake syrup or white or brown Karo) but non-edible fluids as well. One dopes mechanical parts with a lubricant, applies a thick protective coating (similar to paint, only thick) or dopes silage with molasses to seal it and protect the nutritional values from deterioration.
Doping fabric wings on an early airplane would seem to be of similar usage, and I presume with no evidence whatsoever, that our family for that usage the same place early aviators got it.
They say the US and UK are two nations divided by a common language, but the US doesn't have a language, it has hundreds of them!
I seem to recall that when I started college in the mid-60s dope invariably referred to marijuana (if not to the aircraft variety, rare in college). In about 1968 or so the Furry Freak Brothers comics appeared, with a focus on marijuana, and introduced deep philosophy like: "Dope'll get you through times of no money better than money will get you through times of no dope." Opiates were nearly unknown on our campus.
Peter
Hi, this is Sarah from Sarah on Sabbatical (the blog that you referenced above). Thank you for reading and including my post in your article 
Here is a direct link to the article on language acquisition for anyone who would like to read the full article: http://sarahonsabbatical.blogspot.com/2013/05/a-strange-form-of-speaking-notes-on.html
Welcome, Sarah. And thanks for the great info. I have had lots of experiences similar to the ones you describe. It's great to know we are not alone. Now I don't feel nearly so brain-damaged.