When ds was in NICU for 2 days, dd (then 19 mos.) wasn't allowed in because she hadn't had chicken pox and hasn't had the vax.
She was generally allowed on the birthing center floor, as were children of unrelated visitors.
When ds was rehospitalized at 10 days old, in a different hospital, dd was allowed to go just about anywhere -- they never asked for her vax status. They just wouldn't let her stay overnight, despite the fact that we're still nursing.
: But that's another rant altogether.
So I'm guessing it depends on the individual hospital what their policy is.
EDIT: Rereading and seeing that you weren't asking about hospital policy. My feeling is that if your ds is generally healthy and breastfed, and you watch where he is and wash his hands after, he should be fine. If his immune system is already down because he's getting over a cold or something, then I'd keep him away from the hospital. But while hospitals in general are "sick" buildings, the birthing area is usually a different matter. The "patients" there aren't usually ill and I know at the one here, the staff doesn't work anywhere else except in the birthing center wing. I'm more worried about my children visiting my husband at his office than a friend in the birthing center at the hospital -- at least at the hospital people wash their hands more often.
