Yes, sadly, you can die from throat cancer. Your chances of survival are better the earlier you catch it. I found some details from the NIH, which says that 90% of people can be cured, if they get diagnosed in the early stages.
It's tougher, 50 to 60% cured, if it's already spread to other parts of the neck or head, like the lymph nodes. If it's spread beyond the head and neck, then sadly, it's fairly likely for the patient to die from throat cancer. At that point the focus is usually on treating the symptoms and trying to make life as comfortable as possible.