No, no and no. Do NOT put any conditioner on Doooney pebbled leather..
I have bags that are over 20 years old and they are still in great shape. Sometimes the leather trimming the bags could,use some conditioner as this leather has been treated differently and will eventually fade and crack.
I have even put a little shoe polish on the trim of some old bags, but never on the pebbled leather. Pebbled leather is always naturally waterproof.