Generally the more grounded copper you have on the board, the better. If you can go to a 4 layer PCB instead of a 2 layer, this will make your life easier. A 4 layer PCB is generally more sympathetic than a 2 layer board to poor board layout since the ground planes in the middle of the PCB stop interference transmitting from the top layer tracks to the bottom layer tracks.
However, if you have a fast moving digital track on the bottom, underneath a sensitive analogue track on the top layer, with no ground plane in between, regardless of the amount of copper on the top and bottom layer, you will get noise on the analogue track.
Good poor layout is a black art. You need to consider not only the amount of copper you have, but also the placement of the components
For good quality analogue, keep the digital ground separate to the analogue ground and bring them together at one point, where the digital return currents do not pass under the analogue components
If the ADC has an evalution kit to go with it, try getting hold of the PCB layout files for the evaluation kit for the ADC. This will normally have been laid out by someone who knows what they are doing and will point you in the right direction