I don't believe it does not, so you are left with trying to create a calculation - there are some excel macros out there that you could use as a start possibly. Also if you could find a conversion table you could join the two tables and have the Hirji equivalent. However, the date functions would not work.
Excel has a simple date format conversion - we have to convert it to a text string as otherwise the underlying date value does not change regardless of how you display the date.
=text(cell with Gregorian calendar date,"B2mm/dd/yyyy")
You could also change this to dd/mm/yyyy, but I needed the mm first so Tableau did not get confused with my US date format.
We can then use that within Excel to create new columns (via vlookup), or include it as another sheet and do a join on the data as in the attached. Now we have the text string. If you try to convert this to a date it within Tableau the date functions seem to work okay. The only issue is when the date is the 29th Feb in a Gregorian year when there was no leap year. You may be better keeping this as a simple text string.
Here's a tbwx with the join. I guess you could also use blending instead of a join (this would be the only option if your data was not text or Excel), plus the Excel file with the conversion formula.
There are also database functions to do a conversion: http://blogs.msdn.com/b/wael/archive/2007/04/29/sql-server-hijri-hijra-dates.aspx
You would want to bring these in as text otherwise you will end up with the same leap year problems.