My sister says she has narcolepsy. Are family members more likely to get the same thing?

Yes. Narcolepsy is a genetic abnormality and can occur in multiple family members although many single isolated cases also occur. Symptoms generally begin in adolescence. There are tests that can be done to see if you have the genetic susceptibility to narcolepsy, but they don't necessarily indicate you have the condition.
Yes. Immediate family members of people with true narcolepsy are more likely to have narcolepsy and other disorders of excessive sleepiness. However, many people with "narcolepsy" are just excessively sleepy, and they should have a thorough evaluation by a sleep specialist.
Possibly. There is a genetic connection with narcolepsy, meaning it can run in families. However, having the genetic risk alone is not sufficient to cause the condition. Some other unidentified event appears needed to trigger the development of narcolepsy. Has your sister seen a sleep specialist yet? That would be necessary to make the diagnosis.