How much do I need predelivery consult with anesthesiology?

Depends.. Most patients are regularly seen by anesthesiologists or certified nurse anesthetists immediately after hospital admission to discuss whether or not to administer general or regional anesthesia for surgery;epidural or no epidural for normal labor. A consult is made earlier if you have a history of anesthesia/surgery related problems, including other members of your family.
It varies! If you and your baby are healthy with no problems during pregnancy, it will probably be fine to meet the anesthesiologist once you are in labor. If you have any unusual health problems or specific concerns, it would be wise to meet with the anesthesiologist ahead of time. Problems with the heart, spine, lungs, or other serious illnesses should definitely be discussed in advance.
Advised. Labor is notoriously difficult to plan. Consulting with anesthesiologist can reduce their time doing paperwork, answering questions, drawing labs, etc., that can delay epidural placement. If you have certain medical conditions, it could be life-and-death. If you are not going to need anesthesia services like epidural, c-section, you may not see an anesthesiologist unless emergent.
Rarely needed. The pre-delivery consult would only be needed if you have had a specific problem in the past that you need reassurance on. Or if you have a specific medical condition that is going to need to be discussed (scoliosis, rods in your back, etc).
Depends. If you are healthy and there are no history of anesthetic problems with you or in your family you do not need to see anesthesiologist in advance. Your obstetrician will arrange for anesthesia consult if there is history of the problems or there is a concern based on your medical issues.