Why would an UPDATE SET REPLACE() statement match rows, but change none and give no warnings?

REPLACE does not play with wildcards that way. I think you meant:

UPDATE [table] 
  SET [column] = REPLACE([column],'TLD.com','TLD.org')
  WHERE [column] LIKE '%TLD.com%';

You have no WHERE clause, so it tried to update 618 rows, but it did not find any instances of %TLD.com% in that column. To see which rows should be affected, run a SELECT instead:

SELECT [column], REPLACE([column], 'TLD.com', 'TLD.org') AS new_value
  FROM [table]
  WHERE [column] LIKE '%TLD.com%';