What is the size of currently-existing tmp tables in innodb?
The only way to see the temp table needed would be to micromanage the process.

Here is how:

USE mydb
CREATE TABLE anonymized_table_name_new LIKE anonymized_table_name;
ALTER TABLE anonymized_table_name_new ADD COLUMN `anonymized_column_name` VARCHAR(100) NULL;
INSERT INTO anonymized_table_name_new (list of all columns except anonymized_column_name)
SELECT * FROM anonymized_table_name;
ALTER TABLE anonymized_table_name RENAME anonymized_table_name_old;
ALTER TABLE anonymized_table_name_new RENAME anonymized_table_name;
DROP TABLE anonymized_table_name_old;


After the third command you can run

SELECT (data_length+index_length)/power(1024,3) tmptablesize_GB
FROM information_schema.tables
WHERE table_schema='mydb' AND table_name='anonymized_table_name_new';


This may not be all that useful because anonymized_table_name_new may be about the same size as anonymized_table_name since anonymized_column_name has no value. Notwithstanding, you would run that query to see the temp table size in gigabytes.