Is it possible to programmatically call, access, or get results from the Unity Dash?
Solution 1:
You can certainly add search data sources (we call them "scopes") for the Dash, and lenses through which to view them. Scopes can also add results to existing lenses.
I don't know that there is an API today to invoke the dash on a particular lens programatically, but it's a very good idea that such an API exist. I like the example you give of having an indicator which has a menu item that leads to a lens very much.
So, please file a bug, feel free to copy this comment in for support, and patches welcome.
Addendum: bug #896402 has been filed.
Solution 2:
It should be possible. You can have a look at the 'documentation' here (python) or here. Maybe you should file a bug report that the documentation is less then incomplete.