> Does it mean GDAL cannot handle 8-bit signed int?
There's no dedicated type for 8-bit signed int indeed. The hack used is to still use GDT_Byte but advertize PIXELTYPE=SIGNEDBYTE in the IMAGE_STRUCTURE metadata domain of the band. See http://gdal.org/gdal_datamodel.html
Statistics computation should take that into account to properly interpret the values as signed, but apart from a few drivers (from a quick search GTIff, netCDF, HFA, EHdr, ERS, MEM) that correctly interpret/set the PIXELTYPE=SIGNEDBYTE hint, other drivers will generally ignore it.