I want to put a Canvas with an image in my window, and then I want to pack widgets on top of it, so the Canvas acts as a background. 
Is it possible to have two states for the pack manager: one for one set of widgets and another for another set?
The answer to your specific question is no. You can't have two states or otherwise use pack two different ways in the same parent. 
However, what I think you want to accomplish is simple. Use the built-in features of the canvas to create an image item that is part of the canvas, then pack things into the canvas as if it were a frame. 
You can accomplish a similar thing by creating a label widget with an image, then pack your other widgets into the label.
One advantage to using a canvas is you can easily tile an image to fill the whole canvas with a repeating background image so as the window grows the image will continue to fill the window (of course you can just use a sufficiently large original image...)
How do I overlap widgets with the Tkinter pack geometry manager?