What is and isn't possible in relation to SOAP (Simple Object Access Protocol)?
The Zendesk API is a REST API. It doesn't support using SOAP to create, retrieve, update, or delete Zendesk data directly. However, you could feasibly use middleware to use SOAP with the API.
You can call external SOAP APIs from the Zendesk Apps framework. For instance, you could use SOAP to pull customer data into the ticket or user sidebar in Zendesk Support.