Kelompokkan berdasarkan bulan atau 0 jika tidak ada hasil?

Anda tidak perlu "membuat tabel dengan nilai 12 bulan". Anda bisa melakukannya di kueri:

SELECT m.mon, COUNT(i.date_added)
FROM (select 1 as mon union all select 2 union all select 3 union all select 4 union all
      select 5 union all select 6 union all select 7 union all select 8 union all
      select 9 union all select 10 union all select 11 union all select 12
     ) m left outer join
     invite i
     on m.mon = i.month(date_added) and year(date_added) = 2013
GROUP BY m.mon;