I would be hurt not to be notified, but I'd also be OK with it.
The *biggest* reason I'd be hurt is that I think I *can* say, "Do you want me to come over? Shall I some see you guys in the hospital, or is that overwhelming?"
And I'd be hurt because they'd be deliberately shutting me out of one of their most joyous moments, and I'd worry that they didn't love me, or that they felt they needed to protect themselves from me.
However, if I were a pushy person, I'd be even MORE upset, because--well, I'd be pushy and have no sense of boundaries, right?
I got descended upon with Kid No. 1--I looked up during visiting hours, and there were 25 people in my room, no joke. All people I loved and whose presence was perfectly appropriate, but it was all of them, all at once! (C-section, so I was in there for a few days)
For Kid No. 2, esp. since it was a premature birth, I told my MIL that she could *tell* people in the family, but that nobody was to visit. (Another C-section, so again, in there a few days, but not really comfortable.) Well, *she* could visit, but not the other people.
But I could *trust* her, and I could *trust* the other relatives, to respect the boundaries I had set. I could say, "well, come and meet the baby, but then go home," and she'd do it.
If you can't trust people to respect your boundaries, then I think you'd have to almost flat-out lie to them. Which is too bad. (and there you go--respect preserves honesty; lack of respect destroys it)