I don't think this is possible in Tableau Desktop, and can't see any workarounds. All new connections are done through manual steps.
Dimitir's right, this isn't possible.
Workarounds? Well, I guess there's one, which would work as long as the URLS conform to a pattern, and you can produce a separate workbook for EACH raw level data connection (and you are using Tableau Server).
Let's say your urls are like this:
And you name your workbooks like this:
You'd publish your master workbook and all raw data workbooks to Tableau Server. Your raw data workbooks would end up with Tableau Server URLs like this:
What you need in your Master Workbook is a calculated field that creates a Tableau Server URL based on the name of the dataset. Something like:
"http://yourserver/views/"+[raw data name]+"/Sheet1"
As new raw datasets appear, you just need to publish a new workbook that connects to the raw data.
Does that make sense?
PS - i like your question: what if one could create a generic worksheet/dashboard and control dynamically which datasourse it uses. Nice.