Mdate does not support any dates beyond the beginning of the current epoch (longcount 0.0.0.0.0) matching with the Julian Day Number correlation, including Gregorian dates. However, you can have fun with correlations, for example:
$ mdate -c 584285 -j 584285 '+@J @d @m @Y @l @h @t'
584285.0 13 08 -3113 00.00.00.00.00 8 Kumk'u 04 'Ahaw
However, the Mayan date above is meaningless :)