Are people with narcolepsy always tired or could they just have a day every week or two where they feel like they're going to collapse and sleep?

Yes: Narcolepsy can occur daily or periodically, such as one or more days per week depending upon numerous factors. The most common cause is obstructive sleep apnea, leading to excessive daytime sleepiness and narcolepsy, but the narcolepsy can occur every day or periodically on some days.

Frequently fatigued: Fighting being tired can be a daily effort for those with narcolepsy. Good treatment lessens the symptoms of fatigue, but most patients have lower quality of life scores than normal people because of fatigue.