Answer
ArcGIS supports raster data that is 12 bit held in a 2 byte (16 bit) container. However, if a raster only has 12 bits per pixel, then it is currently not supported.
For example, Space Imaging and Digital Globe create 11 bit rasters that are held in a 16 bit container. This means that out of 65,536 values possible, only 2,048 are utilized.
Note:
Space Imaging, such as IKONOS and Digital Globe images are supported by ArcGIS as these are both 11-bit datasets.