probably not. the compressor will flick on once it gets below about 100psi in the tanks and will stay on until it reaches the cut-off valve point or the truck is turned off. if you ever are near an idling truck and hear a loud PSSSHHHH that's the air dryer going when the compressor cuts out (this is just to keep moisture out of the tanks).
I think the compressor works faster to fill the tanks than the horn drains them. when I drove truck I would get bored and just raise and lower my seat for hours (this runs on air pressure) or blast my face with the air gun (this is a pretty standard accessory) and I never saw it get below eighty or so psi in the tanks. the only time it really crashes in when there's a massive leak somewhere or you forget to attach one of the brake lines. of course if you dont attach the red line the trailer brakes will stay locked up so that's another sign too.
tl;dr, it may be posssible with a weak enough compressor but practically it would never happen. it would take at least a few minutes of just laying on the air horn.>t. drove trucks for a couple years after college to pay off loans