They replied:
Currently there is no Revit API for getting the Publish info including the date.
The Revit UI (Revit Home) shows this info, so such an API is technically feasible.
You might want to submit a wish lis item for it in the Revit Idea Store.
Whenever you require new or enhanced Revit or Revit API functionality, the Revit Idea Station is the place to go.
Please search there for a corresponding wish list entry for the suggested functionality and add your comments to it, or create a new one, if none already exists:
https://forums.autodesk.com/t5/revit-ideas/idb-p/302
Tag it as an API wish:
https://forums.autodesk.com/t5/revit-ideas/idb-p/302/tab/most-recent/label-name/api
Ensuring that a wish gets as many votes as possible helps underline its importance to you and the rest of the developer community.
The Revit Idea Station is currently one of the main driving input forces for Revit API enhancements.
The Revit development team look there. Your comment here in the discussion forum might be overlooked.
Thank you!