EDP does not have a direct C# API interface to make calls and play announcement but what you can do is use a REST web service on your EDP snap-in. The REST service can perform the operation you like (make call and play announcement) and allow parameters to drive the request such as called party endpoint. Your C# application can consume the REST service.
When you create an EDP snap-in project using provided Maven template, a REST web service is automatically created for you. Refer to MyApplication.java and MyResource.java. The MyResource.java is where you can create/define your REST operation.