Is this a ridiculous idea?

No, I don't think that's weird. It's a great idea, if you have the time to do it. That will let you get the know the environment while at the same time letting the staff and management get to know you. Seems like a win-win to me. Just keep in mind that while you are there, you are a volunteer, not an RN. I would stay far away from any sort of patient care.

Another good way in is to work for the same health system. At my old hospital if an employee wanted to transfer to an open position, the hiring manager was at least obligated to interview them. That way, prime positions were always filled from within the system.

Good luck. I hope you have fun and eventually get an offer!

It's not a ridiculous idea but I'm not sure it can happen, and I'm not sure what you could do if you subtract all patient care opportunities. No hospital I've worked at has ever given volunteers any role in L&D or mother-baby, and the process of putting someone in a patient care area requires a certain level of training, background investigating (especially if you're around babies), etc so it's not as simple as going up there and following people around. If you already work in this hospital you might be able to arrange some sort of shadowing or internship experience. Some NICUs have formal volunteer programs where you come in and hold babies when their parents can't be there. That's the closest legitimate volunteer program I can think of to get you slightly in the door for mother-baby.