Is using async in setTimeout valid?

setTimeout adds a delay before a function call, whereas async/await is syntactic sugar ontop of promises, a way to chain code to run after a call completes, so they're different.

setTimeout has terrible error-handling characteristics, so I recommend the following in all code:

let wait = ms => new Promise(resolve => setTimeout(resolve, ms));

and then never call setTimeout directly again.

Your code now becomes:

let foo = async () => {
  await wait(2000);
  await this._doSomething();
}

except foo waits for doSomething to finish. This is usually desirable, but without context it's hard to know what you want. If you meant to run doSomething in parallel with other code, I recommend:

async () => { await Promise.all([foo(), this._otherCode()]); };

to join and capture errors in the same place.

If you truly meant to fire and forget _doSomething and not wait for it, you can lose the await, but you should try/catch errors:

async () => {
  let spinoff = async () => { try { await foo(); } catch (e) { console.log(e); } };
  spinoff(); // no await!
}

But I don't recommend that pattern, as it's subtle and can be easy to miss.