No, you'll tie your funds up for a week or so and end up with a travel credit, not a refund, anyway.

Once nonrefundable, always nonrefundable. n8-the-gr8 has the correct approach -- although note that it doesn't actually accomplish anything to try to sit on the inventory while you cancel, as he's describing; the fare isn't final until purchase is complete. You're going to be subject to changing inventory between the time that you cancel and the time that you book the replacement flight. If the fare you want is no longer available by the time you get to the end of the purchase flow, you'll get a "fare not available" message and it will ask you to confirm the new price instead.

I tried this over the weekend, and the price of the flight I wanted increased by over $100 between the time that I canceled my old ticket and booked my new one. I ended up just keeping the travel credit and booking my replacement flight on AS.