It looks like "Start application pool immediately" controls whether the application pool is "Started" when the World Wide Web Publishing service is started. But a "started" application pool is not necessarily running (meaning there may not be a w3wp process).
If an app pool is not "started" then you will get a 503 when you hit a site that uses that app pool.
If an app pool is "started" then a w3wp process will service your request. "Always Running" means that when the application pool is started a w3wp process starts. OnDemand means the w3wp process spins up when you first hit a website that is associated with the application (there is a delay while the w3wp starts).