Is there a way to tell a Mac .app bundle to open the command line for the purpose of printing to stdout? I think it does not really matter, but it is a C++ Qt app.
No, there's no way to do that.
An app can launch Terminal.app or similar and make it open a window, but that window won't display the output of the app. The stdout of an app isn't connected to any "command line" or Terminal window or anything. Basically, it's a file descriptor opened to /dev/null. You could re-open it to some other destination, but none will be a command line or Terminal window unless you build it to be so.