I don't see a straight way of doing it, but here it is how I'd do it:
Are you familiar with Drupal hooks? That's the path I'd follow.
The Webform module has some hooks, I'd try with these 2:
- hook_webform_submission_create_alter
- hook_webform_submission_presave
Depending on your needs. Explore webform.api.php, inside the module's folder to see more details.
A simple and generic example:
Create a new module, let's say webform_mailing, then create a function that hooks into the Webform module, like this:
<?php
function webform_mailing_webform_submission_create_alter(&$submission, &$node, &$account, &$form_state) {
// Do your API calls here
}
Your function will run when a Webform submission happens. You can then use the parameters, like the $submission to get the values, call your API and you're done!
Note: Be careful not modifying the $submission, as you see this value is passed by reference, so if you change it you can mess with your form submission data.
I hope this is helpful