Four layer analog board, should I pour ground on top and bottom layer?
The real question is would adding small 1pf-0.01pf capacitors to ground all around my signal trace to ground help? The answer is not really. Sometimes you will need copper pours for super high impedance inputs such as the inputs to the INA116 or OPA129, they have a guard trace that runs around the signal to keep leakage through the PCB. RF is another thing you would have to shield from. A better way to design for low noise in an analog signal chain is to do this:

Select the right op-amp for the first stage amplifier, filter correctly, and minimize your noise in your signal band pass. Once you have the signal amplified, it doesn't really matter, a 100nV's of noise is nothing to 5V or whatever your rail is. The key is to watch the signal at the input of the board, if you want to be a good low noise pcb designer, think about the pcb in parasitic terms. IE: traces have capacatance between them, and other layers and the pcb also has resistance, it is quite high but still there. A good book is Electromagnetic Compatibility Engineering by Henry W. Ott, that will help you work out the details.