The short answer is: yes. Hurray!
The medium-length answer is: yes, if have mad skillz. Aww, shucks.
A more full answer
Through Google Apps Script, Google Docs is amazingly extensible. The lynchpin function you are seeking is aptly named
addBookmark() (class description here). The function requires a passed value, however, and that is what will require some creativity.
In Pseudo-code, something like the following might work:
Prior to uploading the document to Google, designate the bookmarks you want with super-special-awesome markup that doesn't interfere with anything. Per your suggestion, let's pretend we know that enclosing in two equal signs will not cause you problems, so
== Special text to bookmark ==. Upload the document. Run your script.
- Starting at the top of the file, search the text of the document for a string pattern that matches
== [any text] ==
- When matching string is found, get the
Position (class description here) of the text
- Use Position and run
- Continue with search of text until end of file
- Announce the end of the script execution
For a competent programmer, this is not a particularly difficult task. Even though I can conceptualize the pseudo-code and read the class descriptions, if I tried to write this, I would certainly gain more gray hair.