I had a c-section in May, and despite numerous discussions with my OB consultant and the anesthetist, they both demanded I remove my enhancements. This despite my preparing arguments about alternate ways of checking my oxygen levels (the "finger clip" that people refer to is called a Pulse Oxymeter, which measures the concentration of oxygen in your blood). You can "technically" use a toenail or even an earlobe with this machine, however most hospitals don't carry the attachments to make this possible. While they will look for a change of colour in the nail bed, unless you have a chronic lung condition, it's not the first thing they look for and are more concerned about the pulse ox machine working properly.
I took them off, but pouted about it.
In August, I was back in hospital with a lung condition, and happily took them off as I didn't want ANYTHING to interfere with the Pulse Ox machine - every percent higher on that device meant I was getting better. As we didn't know what the cause was, they were investigating everything.
Anyway, it's up to you if you want to challenge the medical staff about this - it's going to very wildly between doctors. Prepare yourself for a fight, though. A lot of hospitals have policies against all staff and patients wearing "false nails", so the enhancements we build are lumped in with the £4.99 Boots special stick-ons. No concession is made for proper enhancements.
I realised afterward that if I just took a medium buffer and took the shine off my enhancements, they probably wouldn't have noticed they weren't real - as I usually wear clear powder near my cuticle, it probably wouldn't make much difference if I was wearing them or not.