One option would be to integrate the script into the existing plugin code. However, I'm afraid that we are not able to provide support in this forum in regards to customizing the plugin's code, so that I'm afraid that would ultimately have to be researched independently. The plugin code can be accessed by going to the WP Admin page > Plugins > Editor > MailChimp.
As far as alternative implementations, I'm not quite familiar with the script in question, but depending on what information the script needs access to, there may be some other options to consider. For example, if you're looking to have it interact with successful signups only, you may consider using a webhook event (which is available in your MailChimp account).
A webhook will pass the subscriber information to a designated URL whenever a successful sign up occurs:
If I'm understanding the nature of the script correctly, webhooks could be utilized to pass that information to your script and be used in the way you're looking for. Webhooks will fire when a successful signup occurs on your WordPress MailChimp plugin form as well.
If you have any further questions, just let us know!