AWS is rental of server instances. Servers without GPUs. Bitcoin is not cost effective when mining using CPUs, so nobody has done that analysis for nearly two years because its an obvious money loser and becomes a worse option with each passing day of rising difficulty.
Now EC2 (compute cluster) does use GPUs but NVidia GPUs which don't perform at a fraction of the level of AMD GPUs for the specific purpose of Bitcoin mining. Although it was not analyzed recently, a calculation from a while ago provides numbers in the right ballpark, if not better than they would be today. In that study costs you more than twenty dollars of EC2 charges to earn one dollar of bitcoins.
Once ASICs ship that difference will increase possibly by an order of magnitude.
