If I follow your statement, it doesn't appear correct. JS Promises are eager, and the work underlying the promise will begin executing prior to being awaited. Await is just blocking on that execution's resolution.
// Given:
const fooPromise = asyncFoo();
const barPromise = asyncBar();
// Then this...
await fooPromise;
await barPromise;
// ...is equivalent to this:
await Promise.all([fooPromise, barPromise]);
Now, Promise.all() is useful, but it is unrelated to when computation starts.