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It is possible, but you need to implement the SATA functionality in you uController.
The most important attribute of SATA is its speed. If you're intending to do such thing, then be sure to meet the minimum requirement by SATA.
In fact, you migh be needing something more than a uC, like a powerful FPGA or something...
It is possible that SATA communication controller are available as ASICs, that might ease your job.