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Yes, but I suggest pour copper on either layers for GND if you can manage power with fat traces rather than layer/ pour island. Having a bigger ground is better from the system performance point of view.
I would agree if only one voltage for the power layer, otherwise I would go with ground every time.
---------- Post added at 13:43 ---------- Previous post was at 13:38 ----------
Oh as to the reason why not to have a top power and bottom ground on a two layer board, you will be effectively creating areas of copper connected with high impedance routes, these could act as diopoles and cause EMC problems. It would also create some very interesting return paths for signals as they would be couple with the plane they are adjacent to. So my view would be ground as both top and bottom pour, with power tracks, would be the best choice, and least problematic.