How to bypass CAPTCHA during Behat functional testing?
Using the API Driver you can, as you say, modify CAPTCHA After threshold and restore it at the end of test, but you need to execute tests in the same machine.

If you want to do it form another machine you have to set up a way to alter that variable from outside. You can define a hook menu that alters that variable, in a dev module that will not be enabled in production site. You can also set up a drush remote command that modifies the threshold in th remote machine and restores and the end of the test. You can add this drush command in the script that lauchhes behat tests or even inside behat in a behat hook.