At mine, they did the exam while sewing me up (they did a quick exam in the OR, then did a proper one in the nursery after showing me the baby... I was ok with this because I knew closure would take a while), then he joined me back in the LDR for recovery. No big deal, it was standard policy. He was all ready for me when I was wheeled in. I really liked that they did my pre-op and recovery in an LDR BTW... felt less like just going into surgery. Last time, I don't think I even saw the regular L&D rooms.
First birth, they also did the exam while I was being sewn, right next to the OR. That wasn't in the USA though.
I'd say my hospital was pretty middle of the road... not "crunchy" in any way (they would not have allowed a dropped drape or breastfeeding on the table), but they seemed into updating their policies and procedures in line with current practice. So routine baby exams were done in room, they did couplet nursing, night nursery only, that kind of thing. It's certainly not out of line for you to ask but hospitals can be surprisingly inflexible about policy. The other hospital here used to have a mandatory nursery stay--I've heard they've changed some policies recently, but I don't know details. Certainly, that was in effect a year or so ago, so if it has changed it's very recent, and I know other hospitals that still have old fashioned policies.