Will a promise exit the execution prematually without await?

Here is how the await is used:

The keyword await makes JavaScript wait until that promise settles and returns its result.

If app doesn't want to await until a promise settles and returns (such as update non-critical backend database), is it OK to call the promise without await? May a promise called without await exit prematurely before the promise is completely finished?

from Will a promise exit the execution prematually without await?