Are analog planes necessary for my circuit?
Probably not, the only time you should split planes is if you have currents that would generate voltages large enough to be seen by your ADC.
0.5oz copper is about 1mΩ/in^2 so it would take a large amount of current (50mA) to generate anything that a 16bit ADC could see (to change even 1 bit). (currents run from the source back to ground on the ground layer of the PCB)
Even with a large current, the layout can be change to redirect the current, so don't split the plane.