Yeah definately do lots of tests pieces until everything is exactly how you want it to be before using your case. The depth of cutting shouldn't matter as far as I know. The curves you are talking about; are these the curves that appear towards the back of the case where the AV and power plugs in? Where, if the case was horizontal, the flat part begins to curve until at 90 degrees? I don't think the CNC router would have a problem with that, just set it to cut against the machine bed all the time and it will cut into the curves. As most of the case is flat and the curve is relatively small, I would say that the image won't be distorted at all.
Or if you mean the curve going across the console (when horizontal) just measure the top, bottom and middle dimensions and make your deisgn fit in between that