In a pregnancy where the baby is breech, does the doctor try to invert the baby's position?

Maybe. You can either do a version or most likely for what is best for you have an elective c/s for breech. Some patients depending on the number of previous deliveries might even attempt a vaginal delivery. Talk with you OB and a plan of action between you and your OB can be determined.
Breech. External podalic version is the process by which an OB will attempt to change the presenting fetal part from breech to vertex. This is a process done in a hospital by a skilled ob. The overall success rate is approximately 70 %. Many factors go into determing which patient is a candidate for this procedure.