I doubt it would work without an alarm to make you wake up after a short nap. Once you're asleep, you need that aid to wake you up. Otherwise, your body will stay "shut down" for as long as it needs to. If this approach doesn't make you more productive, it will surely make you more cranky!
I heard a doctor on TV say that your heart needs deep sleep to "rest". So, do whatever you want. You only live once.