Without taking into account whether it is possible or not (because it is obviously possible) I think that function shouldn't work that way. The reason is just dependencies.
The qa_q_path() function currently has no dependencies and can return the values it is looking for on it's own (as the rest of the functions in that file, with the exception of the plugin-loading-related functions). I'd leave it just like that. Adding a database access would force the function to depend on the database. That could leave to unexpected errors because the implementation wouldn't be so predictable for developers.
The suggested feature could, however, be implemented just in a helper wrapper. That could be in another file (in general, very originally called, helpers.php). That generic-purpose file could contain a qa_q_path_full() function that would work exactly as you suggest. Furthermore, you don't need that in the core. You could just have that file in your own plugins.
Finally, and maybe I'm just talking about my experience, I don't think there are so many situations in which I wanted to display the full URL and didn't have a question array in context to get the title from. In fact, I've only faced that once, which means, the qa_q_path_full() function would have saved me a line (to fetch the title from the DB) and also would have added a line (to require the helpers.php file).