Power supply for battery powered application with precision ADC
You didn't mention any current requirements for you device nor the overall voltage ranges for the balance of your circuit. You may wish to update your question with this information in order for the answers to reflect a more comprehensive perspective.

The ADC will have an internal voltage reference that will mitigate basic ripple issues as long as the rail supply is above its minimum VIN. I would be much more concerned about noise from the switcher getting into the analog front end of the ADC, particularily with the ~120 dB dynamic range with which you are working.

While switcher noise issues are not insurmountable, I would favor a design with a cell chemistry/count that eliminates the need for a switcher. Examples would be a rechargeable LiPo cell, 3.6 volt primary lithium cells, or 3 'N' type 1.5 volt alkaline cells. These combined with judicious power management of LPOs, if needed, would provide an electrically quiet device.