Does Narcolepsy that Riki had really exist?
Riki's parents died when he was around ten years old, leaving him in a state of depression. Around the same time, he was diagnosed with narcolepsy, a disorder causing Riki to uncontrollably lose consciousness at random intervals.
New constructed worlds would be formed again and again, with Riki repeating events, becoming stronger each time.

Taken from Little Buster's Wiki.
It seems to me, that in the beginning he definitely still had narcolepsy, but he might have overcome it at the end through the process of becoming stronger.