I've taken Aleve many times and never felt sleepy, however, I'm a firm believer in medicine reacting differently in different people.
I tend to have the opposite reaction from many medicine. Bonine, for motion sickness, makes me VERY sleepy (like totally out of it for 24 hours--strange!), but it's supposed to be non-drowsy and most people take it without problems. I also tend to be very sensitive to medicine and tend to half dose things like cold medicine.
T&B