What are the chances of having damaged tendons from an accessory navicular bone? My dr said he might have to do a tendon transplant.

Navicular. The posterior tibial tendon inserts into the navicular bone. If there is an accessory navicular the pt tendon is affected however not torn. The procedure is called an kidner procedure to remove the extra bone and reinsert the pt tendon. I would encourage you to get xrays and an MRI prior to surgery as well as a second opinion.
This can occur. I'm not sure i'd refer to it as a transplant. What commonly is done is the accessory bone is removed and then the affected tendon repaired and or reinserted.