I doubt it.
That said... I lived in a dorm room for a year that absolutely REEKED of Pot. The whole building did. (Hadn't been renovated, ever, and was about 30 years old. The next year they renovated it
and I'm told it doesn't smell of pot anymore, but they tore a huge chunk of the drywall out to get rid of the smell.)
We had a 'Plug ins' air freshener, the biggest one they had. 3 of them, actually. They were supposed to cover 500 sq ft, IIRC, and we had 3 of them in less that 300 sq. ft. (4 people). And you could STILL smell the pot when one of them needed a new cartridge. And none of the 4 of us touched the stuff, so WE weren't adding anything to the system. I'm sure other rooms were, but we weren't.
If ANYTHING would have caused a false positive, living there would have.