Yes, at least the "main" or "update" method of the current scene is run every frame.
If you look at the Main script, you'll see a 'while' loop that runs $scene.main
Above that, $scene gets set to Scene_Title (Which creates an object of that class, and assigns it to $scene)
In the main method of Scene_Title, it reads in all of the rxdata, sets up the menu, then runs a loop containing:
Graphics.update # refresh screen & advance 1 frame
Input.update # check to see if there is any input from the keyboard
update # If the Action key is pressed, execute the command currently chosen
When you select New Game, the $game_* data is set up, and the $scene is changed to Scene_Map.new, so the Scene_Title object disappears (is disposed), and a new object (Scene_Map) is created, and now it's main method runs.
Why do you ask?