If tonsillitis spreads throughout the body can you die?

Sepsis: If a bacterial tonsillitis were to spread into the blood stream to cause bacteria in the blood it could certainly become life threatening.

Separate issue: Tonsillitis is a infection focused in the tonsils. If bacterial, it is a surface infection, meaning it has not entered into the blood or deep structures but stays in the regional structures of the upper airway, mouth and neck. When tonsillitis is viral, like mono & it can enter blood but is rarely more than inconvenient. In theory, if you have a weak immune system, any infection could kill you.