Hi Lance, if I understand your post correctly, it sounds like the data is already being stored in MongoDB and the difficulty is in either connecting to it there or being unable to connect directly to the web service that's writing the data without using a WDC.
Since you made this post Tableau Desktop 10.3 has been released- including a native connector to MongoDB. Take a look and see if the native connector might meet your needs.
I looked through the Ideas forum and found some posts that sound similar to what you're describing, but in most cases WDC is the solution. I'd recommend searching to see if you can find an idea that is similar to yours and give some more information about the proposed use case, or create a new idea.