If any living thing consumes enough of a poison it will die. But I feel that is not what you want to ask.
Perhaps you meant to ask if a snake will die if it drinks its own venom? That would make more sense as a question.
In English, **venom** and **poison** mean different things when talking about a toxic chemical produced by an animal.
**Poison** is a toxic chemical produced by an animal that is meant to be ingested/eat/drink.
**Venom** is a toxic chemical produced by an animal that is meant to be injected into the bloodstream.
So a snake bite has venom, but a colourful tree frog has poison on its skin.
Venom is _typically_ not nearly as harmful if ingested, even if by a different animal, because it is meant to act directly in the bloodstream