yes, as long as you sync some music to your Apple Watch, you can listen without your iPhone with you.
However, you won't be able to track how far you ran without your iPhone as the Apple Watch does not have a GPS. Since the AW learns over time the more you wear it paired to the iPhone, theoretically it will learn your stride and movement and could potentially give a somewhat accurate distance based on step count, height and the data it's collected on you. But that's all hypothetical.
If you want distance run, you need your iPhone with you. Otherwise, all data collected while you run gets synced when you come back into range.