This is possibly intentionally referring to a singular group supply. Likewise, in a household or workplace, you could say that you had some of "the coffee", if you were partaking in the household or workplace group supply.
It was from a comedy podcast where Conan is always using intentionally silly terms for that. I think they were just riffing on that, intentionally making it sound stupid.
Pedantry: the theory th' interwebs give me is that the evil weed has also been known as "pot" since the 1920s, and its use, without determiner, is attested in print as far back as 1938, so I doubt that extraneous determiner would be anything but intentional.
Yeah I'd say it's almost certainly veiled in irony given the context. Something derived from reefer madness stylization. I do it as well, quite literally using that phrase. Tinges of unguided parentalism and the vogue surrounding it - otherwise ignorance.
The use of the definite article before the word "pot" really gives that sentence a "How do you do, fellow kids?" vibe.