You could try comparing the nvarchar string to the string cast as varchar.
DECLARE @str1 nvarchar(20)
,@str2 nvarchar(20)
SELECT @str1 = N'AB' + NCHAR(12354) + N'CD'
,@str2 = N'ABCD'
IF @str1 <> CAST(@str1 AS varchar(20))
PRINT 'Str1 contains unicode character'
ELSE
PRINT 'Str1 contains no unicode'
IF @str2 <> CAST(@str2 AS varchar(20))
PRINT 'Str2 contains unicode character'
ELSE
PRINT 'Str2 contains no unicode'