How to output a boolean in T-SQL based on the content of a column?

You have to use a CASE statement for this:

SELECT CASE WHEN columnName IS NULL THEN 'false' ELSE 'true' END FROM tableName;

Or you can do like this:

    SELECT RealColumn, CAST(0 AS bit) AS FakeBitColumn FROM tblTable

If you need a output as boolean

CAST(CASE WHEN colName IS NULL THEN 0  ELSE 1   END as BIT) aIsBooked

for the column in the view you can use something like

CASE WHEN ColumnName is not null THEN 'True' ELSE 'False' END

or in a statement

SELECT 
s.ID,
s.[Name],
CASE WHEN s.AchievedDate is not null THEN 'True' ELSE 'False' END [IsAchieved]
FROM Schools s

or for further processing afterwards I would personally use

SELECT 
s.ID,
s.[Name],
CASE WHEN s.AchievedDate is not null THEN 1 ELSE 0 END [IsAchieved]
FROM Schools s

I had a similar issue where I wanted a view to return a boolean column type based on if an actual column as null or not. I created a user defined function like so:

CREATE FUNCTION IsDatePopulated(@DateColumn as datetime)
RETURNS bit
AS
BEGIN
    DECLARE @ReturnBit bit;

    SELECT @ReturnBit = 
        CASE WHEN @DateColumn IS NULL 
            THEN 0 
            ELSE 1 
        END

    RETURN @ReturnBit
END

Then the view that I created returns a bit column, instead of an integer.

CREATE VIEW testView
AS
    SELECT dbo.IsDatePopulated(DateDeleted) as [IsDeleted] 
    FROM Company