we did (though last time it was unplanned) and will this time.
she: wasn't allowed in surgery, but waited with the family. she helped enforce our wishes with visitors and helped with breastfeeding (we had a rough go of it) and would go get things, bring us things, help us, stayed with me when dh had to leave to go take care of our animals, etc.
she helped keep me calm before the surgery, too. maybe many of those things a family member could have done, but it was much easier for us to have the doula, just based on the relationship i have with most of my family. she enforced hand-washing rules, etc. for people holding the baby, and most importantly of all, came home with us. she cooked us something nice, straightened up a bit, etc. and i was so grateful for her help.
she also helped us with the placenta encapsulation- the person who did ours said it was illegal for her to transport it in a raw state (?) and the doula took it home/to the placenta preparer, and videotaped the process for us, as well as having taken photographs in the hospital, etc.
if you can have another person in the OR, she/he can take photos, too, and rub your neck, etc. and perhaps tell you what's happening if you don't want to view the birth. it was absolutely worth it for us, we love her.