Vertigo itself will not kill you.
However if the vertigo is a symptom of a heart attack, stroke etc then it could kill you.
Or if the vertigo leads to you falling when you pass out or something then you could possibly get killed when you fall due to the vertigo.
Mostly vertigo is not a very serious condition and will usually cause not other health issues or death.
However treatment for the vertigo can help but you cannot be fully cured of vertigo.
If you do start feeling dizzy with the vertigo then you should lay down or sit down to avoid falling and possibly injuring yourself.
Also when you think you're gonna have vertigo then you should also avoid driving.