I have been narcoleptic since high school. I was only diagnosed with it 8 years ago (I am ~40), so I actually lived with it for around ~15 years undiagnosed. In that time, I graduated high school, college, and went into a career.
So, with the preliminaries out of the way, and in a effort to contribute to the AMA comm:
Most people with narcolepsy can still drive.