Hello! I had to delurk so I could respond to this. My son was born premature at 31 +1 weeks. Because he was doing so well they didn't discover until two days old that he had an imperforate anus. It's not as uncommon as you may think right now and in your journey you will undoubtedly meet many people who's children are going through the same thing.
We were transferred up to St Thomas Hospital in London where he has had fabulous care. The first year is an adjustment. He had a stoma put in and was in the NICU for a couple of days before being transferred to SCBU.
You will be given a stoma nurse who will teach you how to change the colostomy bags, etc. It's really daunting at first. But soon it will become second nature. I have a plastic chest of drawers where I kept all his supplies next to a changing table (a must) pre cut and ready to just clean him up and slap a new one on as quickly as possible.
When he was 4 months old he had what is called a pull through. That will be at least 4-7 days in the hospital. It depends on the severity of the imperforate anus as to how intricate this can be. Your baby will keep their stoma in for awhile (months) afterwards until they feel nerves etc will have recovered and then they will close it up and you will spend about 3-5 days in the hospital waiting for your baby's first poo!
Poo will consume your life as children with imperforate anus suffer a lot from constipation. My son is on two different medications for it at 15 months old.
Children with this condition often have different abnormalities so after your baby is born they will have lots of ultrasounds and tests to check. Heart problems can be one but with a small hole in the heart they aren't concerned about (my son had one too that closed up on it's own) that's probably not an issue. My son's showed up as a tethered spinal cord which in itself isn't too bad of an additional issue and eyes are being kept on it now that the imperforate anus is mostly dealt with for now.
My son's case was quite bad and he may suffer from incontinence in the future BUT he is the happiest child in the world. Really amazing considering everything he has been through. Obviously it will be a bit different for your baby as they won't also be dealing with being premature. And I'm sure the doctors have already been over this all with you. For us it was a surprise as it hadn't been picked up in ultrasounds previously.
But if you have any questions or want to talk to someone who has been through it and finally coming out the other side please feel free to PM me. I felt really isolated and unable to talk to anyone about it and of course it was me suddenly having a baby who needed a lot more care than I had expected.
It is so worth it though and really made me a stronger person.
p.s. To your original question... if they are happy to wait for natural labour and that's what you want then go for that. I wouldn't think they'd wait too long though as they may worry about trapped metanium. But that would just be something to talk to them about. I had a c-section and it -did- hinder my ability to spend time with my baby in NICU/SCBU as I couldn't sit there with him for long.