The latter is how caffeine works. Blocks adenosine receptors so you don't feel tired even though you are.
Turning off that misfiring with drugs would be dangerous (pain is an alert) but also improve the quality of life of so many people!
I've only had two instances where I ignored all the signs and continue to push on until my body literally shut down on me. Finals week in college as an architecture student trying to finish a final studio project, and study for four finals. 5 days, 3 hours of sleep. That was one of them.