Is there a way to generate SOAP API requests from actions taken in the Magento UI?
For example, adding a shipment to an order.
This would be helpful for testing the API for a particular site.
By default is not possible. Of course you can build an UI for testing the SOAP API and it doesn't even have to be a Magento extension. It can be a standalone application. But I don't see the point.
I've used this tool before mostly for testing the SOAP API for my custom modules and I really liked it. Very easy to use and well documented.