In the FAA Guide For Medical Examiners there is only a single direct reference to narcolepsy
Under the Obstructive Sleep Apnea QA section it states
Does this process involve other sleep disorder conditions? (E.g.
Period Limb Movement Disorder, narcolepsy, central sleep apnea, etc.)?
No. This process is for obstructive sleep apnea only. If it is clear
that the airman suffers from a different sleep disorder, DEFER and
submit any supporting documentation for FAA decision.
This would indicate that if you suffer from any sleep disorder conditions your medical should be DEFERed
Earlier in the document it states:
Medical conditions that chronically interfere with sleep are
disqualifying regardless of whether a sleep aid is used or not.
Examples may include primary sleep disorders (e.g., insomnia, sleep
apnea) or psychological disorders (e.g., anxiety, depression). While
sleep aids may be appropriate and effective for short term symptomatic
relief, the primary concern should be the diagnosis, treatment, and
resolution of the underlying condition before clearance for aviation
duties.
Narcolepsy is a sleep disorder and would potentially fall under this definition and thus prevent your from getting clearance.
In these cases its usually best to get the advice of an FAA AME.