As at 10.2, as J.Sobetzer noted previously, ArcGIS can read but not write MrSID. Afaik, the request is not possible out of the box unless you licensed the encoder from Lizardtech.
Here is a detailed example of doing almost exactly what you wanted to do, but taking SIDs and outputting TIFFs. It would be trivial to swap the input and output formats.
FMEpedia - Raster Mosaicking Scenario
This of course, supposes you have access to Safe Software's FME...
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