Force a draw - outside of the ::draw() method?

One way to do it is to add a "loading screen shown" variable that is set to false when the loading action is initiated (e.g. by clicking the mouse in the example).

void ofApp::draw(){
  if (state == 0) {
    myfont.drawString("State 0 - click anywhere", 100,100);
  }

  if ((state == 0) && (doLoad)) {
    if (loadingScreenShown) {
      LoadAndInitHeavyHog();
    } else {
      myfont.drawString(" --- LOADING --- ", 100,100);
      loadingScreenShown = true;
    }
  }

  if (state == 1) {
    myfont.drawString("State 1 - loaded...", 100,100);
  }
}

I think this should work, but it does require another variable.