I think some others may have to pipe in here to see what is possible. Once the data is attached to the block, it is not document text anymore, but user text on the definition in the block table. Does this thread help a bit with Python: Can you add User Text to Block Definition?
As for Grasshopper, this is the method to import and read the block definition data (Originally Document data on the external files):
The Block definition userdata sits on the block definition in the block table.
This is a bit of a stretch, but here are is a bunch of code to walk around in the block table in Python: rhinopython/scripts/rhinoscript/block.py at master · stgeorges/rhinopython · GitHub
And this is a great thread on walking through the block table: From Python into Rhino Common
And what is on a Block definition object: https://developer.rhino3d.com/api/rhinocommon/rhino.docobjects.instancedefinition
I am also trying to put a sample together with Python, but still working on it.