I don't think that contacting the nurse manager yourself would harm your likliehood of being hired and might actually increase it. Some human resource areas aren't terribly efficient and I actually had an application lost once. Had I not wanted the job and thought to call later to check up on my earlier app. I would have thought the unit just didn't need me. If I already have a small relationship with the floor that I want (ie. know people who can reference me there or have already even casually met the nurse manager) then I always call. I'm very polite, brief and ask if they might have an opening on their floor for my qualifications. Oftentimes, a nurse manager will be very forthcoming and offer advice or other areas to look which HR would leave you hanging on.
If it's a larger facility they will probably ask you to go to human resources to officially fill out an app. but if you've peaked their interest, they will likely ask HR to put a rush on things so that they may interview you. That's happened to me enough times to feel good about the process. Kinda like already having a foot in the door. Just my 2 cents.