In Windows, Is there a way to determine a notepad files path from an open Notepad file?

There isn't presently a way of doing this in Notepad other then the way you have shown using the 'Save-as' which should show the directory of the file you have open.

That being said, if you want this functionality, you can use a bunch of better applications that are also free. Such as:

Notepad++

Sublime Text Editor

UltraEdit (Might not be free anymore)

These are a few I've used, and all of them will show the directory the file has been opened from in the window name at the top left of the window.

On Windows 7 I found the trick:

You can make a small modification to the opened file and then close the notepad. Notepad will ask, if you want to save or discard your changes revealing the full path to the file being edited :)

Well, I think Notepad only tracks the last directory you made save as for files, However, I recommend to use another program like Notepad++, it is more efficient and will give you many features and it is still free and simple program