Answer:
Turns out the ar-SA culture is the only one to use the Hijiri calendar; all the other Arabic cultures use Gregorian. Here are the different date formats in Arabic (a bit messed up because WMD doesn't support seem to support RTL text).
ar-AE 11 ديسمبر 2008
ar-BH 11 ديسمبر 2008
ar-DZ 11 ديسمبر 2008
ar-EG 11 ديسمبر 2008
ar-IQ 11 كانون الأول 2008
ar-JO 11 كانون الأول 2008
ar-KW 11 ديسمبر 2008
ar-LB 11 كانون الأول 2008
ar-LY 11 ديسمبر 2008
ar-MA 11 دجنبر 2008
ar-OM 11 ديسمبر 2008
ar-QA 11 ديسمبر 2008
ar-SA 13 ذو الحجة 1429
ar-SY 11 كانون الأول 2008
ar-TN 11 ديسمبر 2008
ar-YE 11 ديسمبر 2008
And for what it's worth here's the quick & dirty code I used to generate this list:
Response.Write("<table width=300px>")
For Each ci As CultureInfo In (From c As CultureInfo In CultureInfo.GetCultures(CultureTypes.AllCultures) Order By c.Name Where c.Name.StartsWith("ar-"))
Thread.CurrentThread.CurrentCulture = CultureInfo.GetCultureInfo(ci.Name)
Thread.CurrentThread.CurrentUICulture = New CultureInfo(ci.Name)
Response.Write(String.Format("<tr><td>{0}</td> <td style='direction:rtl;font-size:20px;'>{1:d MMMM yyyy}</td></tr>", ci.Name, Today))
Next
Response.Write("</table>")
Response.End()
More cultures at http://www.massimilianobianchi.info/max/articles/22/UI-culture-list-and-codes.aspx