Can insomnia kill you?

Rarely. There is an exceedingly rare insomnia called fatal familial insomnia that runs in families. It is due to a rogue brain protein that causes brain degeneration like mad cow disease. But insomnia almost never kills although it can lead to sleeplessness and accidents while driving. High blood pressure is now associated with insomniacs who sleep less than 5 hours per night. See a sleep specialist.
Yes. Insomnia impacts the quality of sleep that you get at night. If you are frequently sleep deprived this can affect your glucose metabolism, cardiac function, how your body fights infection etc. All of these factors can contribute to a poorer quality of life and insomnia itself has been associated with a higher mortality risk.
Eventually, yes. Insomnia can be a chronic condition that can lead to obesity, obstructive sleep apnea, diabetes, hypertension, depression and eventually hasten death. There are many ways to fight this condition before it leads down those dire paths. Try drinking a calming chamomile tea before lying down, minimize tv viewing in the bedroom and get in the habit of reading a book (not on e-readers) b4 closing eyes.