Is is possibe to put an if statement on a column, for example, if a field in that column is empty then have it as false, if there is data in there then have it as true.

Yes you can do that.
Here is an example that will check wether a colum "is_valid", which stores an integer value of 1 (for YES) or 0 for (NO), is valid or not and return the string YES or NO accordingly.

SELECT
id,
IF(is_valid = 1, 'YES', 'NO') AS is_valid
FROM test_table

In your case you just want to check if the a column (say "test_column") has a value or not so it will look something like:

SELECT,
id,
IF ( test_column  = '', 'FALSE', 'TRUE') AS test_column
FROM test_table

The column "test_column" must be NOT NULL. If it allows NULLs you could check for that:

IF(test_column IS NULL, 'FALSE', IF(test_column = '', 'FALSE', 'TRUE')) AS test_column