I'm not sure what you mean by "the bit between 0 and 1"..... There is nothing inbetween 0 and 1. There is no 1/2 frame. You have frame 0 and you have frame 1. If you can go to frame 0 in your timeline, you can render it. If you can't go to frame 0 in your timeline, you can't render it. Note that you can always choose what frames are rendered in the Render Globals window, however, so if you choose to render frames 1-120 even though you have a frame 0, the frame 0 will NOT render.

Understand now?