The rotting teeth themselves won't kill you nor will a toothache kill you.
However if the rotting teeth or toothache is caused by a serious tooth infection or gum infection that tooth infection or gum infection can eventually lead to other serious health issues.
Health issues that can arise from rotting teeth or tooth infections and tooth aches include heart disease, heart attacks and possible death eventually.
Tooth infections can also cause a severe gum disease, known as periodontitis which then leads to your teeth falling out.
If you have a toothache that keeps coming back or gets worse you should see a dentist to have it treated because tooth infections can cause serious other health issues.