There isn't much of a learning curve with a lens. The only likely issue is that a shallow DOF tends to bring to surface front/back focus issues. Unfortunately you are unlikely to have time to develop a roll of film to find out if there are any issues.
I'm been at 3 births...
#1, not so dark because he held out til daytime and there were windows with semi-opaque curtains. I had ISO 3200 T-Max in the camera and a 50mm f/1.7 lens, but I don't know what aperture I was using or what shutter speed I was getting. This was with a midwife.
#2, 2 AM, very dark. ISO 3200 T-Max again, but pull processed to 1600. 50mm f/1.7 again. This was with a midwife. I remember the only light being from a bathroom with the door cracked.
#3, 12:30 AM, very dark. We're firmly into the digital era now. ISO 1600, 30mm f/1.4. Getting 1/30 sec for general room shots, jumping up to 1/2000 of baby on the work time (getting ready to rush him off to the NICU (7 weeks early). I think the doctor had a headlamp or something. The room was pretty darn dark.
My experience tells me that pushing to ISO 1600 (or even 3200 for a f/2.8 lens) could be a good idea. However you can decide this on-site when you see the room and have an idea when the moment will happen--just don't change your mind mid-roll. If she's laboring all night Thursday night then you probably won't get much sleep --so be careful not not forget what you went with, because you need to tell the lab!