It should do, you just need to make sure the axis are square to each other and the box frame is only there to support the X and Z axis. I'm in the process of build an i3 box frame myself and I'm using 17mm laminated pine, the only issue I have at the moment is to route a recess in the base board so the Y-frame sits flush. You may have the same issue. With the Y bed, make sure that whatever you use is flat, that's the main reason MDF is recommended.
