Clarizen Support has helped confirm that as of today,
API call outs from Clarizen to external third-party APIs are limited to Callouts (a.k.a Outbound Call Actions) and Custom Panels (Custom UI Panels).
Callouts (Outbound Call - Custom Actions) are essentially a SOAP web service call without a WSDL definition. It uses Http POST to send an XML response to a given URL. It doesn't support authentication. Also, all Callout requests are queued in a job server. You can use it within workflow rules upon triggering DB CRUD events, and even as custom buttons and links. I believe you can also use the REST API to trigger a callout.
• Enables you to call an external web service that can either interact back with Clarizen or with other systems
• Run On - You can run the Outbound Call action on behalf of a specific user. The default is the CurrentUser
• URL – the URL of the web service to invoke.
• Have Token for this Web Service - Allows you to enter a token for the entered web service for user identification purposes.
• Web Service User - You can run the web service call action on behalf of a specific user.
If no user value entered the system will use the default workflow user as defined in the organization settings.
• Send also Session ID - Selecting this checkbox will send the current user's session ID along with the outbound call, allowing instant access to the user's session without requiring a login.
Note: This action's execution is queued in the job server, meaning that it may occur in the background and values will be refreshed after completion
Note: If you are getting a timeout, make sure your web service is available from outside of your organization domain and that you are getting results via the simple HTTP call