Yes it is possible to write a python program to push data received at X2 to iDigi, that can be retrieved by a web application.
Python scripts can be uploaded to the device using the device’s WebUI, iDigi Manager Pro, and iDigi web services API. There is also the Digi ESP (Digi’s Eclipse based IDE) for python development, but I am not sure if this product is supported (says supports X2, but does not specifically say X2 SE).
Python scripts can be automatically started at boot time or manually run from the command line (telnet or ssh), and if supported for this product, the Digi ESP.
I don’t think you (a mere mortal) is permitted to change the Python code in a X2 SE. It is part of what it means to be SE certified - so I have been told.
You should be able to create a PC (or external device) application which fetches data from the X2 SE to display on a web page. Since I haven’t work with SE yet, I can’t offer pointers to starting that work.