単純なcaseステートメントでそれが可能です
SELECT CASE
WHEN DATENAME(WEEKDAY, dateadd(mm, DATEDIFF(MM, 0, getdate()), 0)) = 'Saturday'
THEN dateadd(mm, DATEDIFF(MM, 0, getdate()), 0) + 2
WHEN DATENAME(WEEKDAY, dateadd(mm, DATEDIFF(MM, 0, getdate()), 0)) = 'Sunday'
THEN dateadd(mm, DATEDIFF(MM, 0, getdate()), 0) + 1
ELSE dateadd(mm, DATEDIFF(MM, 0, getdate()), 0)
END