Not born with it. Narcolepsy is a sleep disorder that usually develops over the teenage years. It is likely autoimmune related. There are rare situation when narcolepsy occurs in multiple sclerosis, trauma or brain tumor. Narcolepsy is caused in most patients by a "hypocretin" deficiency in the hypothalamus.
Develops later. Narcolepsy is a chronic condition which causes excessive daytime sleepiness and other symptoms. Most people who develop it are born with a genetic marker which predisposes them to acquire the disorder. However, it takes some additional event, such as getting influenza or strep throat or trauma, to actually get narcolepsy.