Congratulations on your pregnancy!!!
Okay, now for the hard part. Honestly, I think it will hinder your chances at the position. Most NICU new grad programs include classroom time as well as one on one precepting on the unit. They usually only do this once or twice a year, depending on the unit. So really, letting you start at a different time than the others might not be an option. Also, the first few months in the NICU are very important - there is a huge learning curve since you really don't learn much about neonatal care in nursing school. Even if you get most of the orientation under your belt before the baby, having an interruption at that point when you go on leave can make you forget much of what you've just learned. It's just a rough situation.
Being in your third trimester AND starting a new stressful job might not be a good match either. Is there any way you could wait to start working after the baby is born? Remember that most hospitals in the US do NOT provide paid maternity leaves, and even those that do usually don't offer that until you've worked there for a year or so. You usually have to use your paid time off (sick and vacation time) which as a new employee you won't have time to build up. So money-wise, it might not make much of a difference to start before the baby. Do they have a new grad program that starts in the winter for December graduates? That would be PERFECT for you! Or maybe they can work something out like you can work in the regular newborn nursery (shorter orientation) at first and then after you've had the baby you can be transferred to the NICU the next time they have a new grad orientation...
I wish you luck.