The myth goes that if you use nitrous oxide in your car, the person behind starts laughing, under one condition, they have the AC on.
Is this possible?

No. The Nitrous is added to the fuel in the engine's combustion chamber to dramatically increase the oxygen content and thus the "force" of the detonations pushing on the pistons - making the engine more powerful. Ergo, what comes out of the exhaust, (and presumably, therefore, into the following car's AC,) is not Nitrous Oxide anymore - it's nitrogen, carbon monoxide, carbon dioxide, water and other combustion by-products.