To call or not to call?

Hi everyone. Hoping to get a some advice. I've been an RN for a little over a year now. For about the past 8 months I have been working part time at a Public Health Clinic (due to this economy it's all I could find) while still actively looking for work at the hospital. I've also been caring for a child with specials needs off and on while looking for work. Like many new nurses out there, I have been unsuccessful in finding a hospital job due to "lack of experience", hiring freezes, etc. Recently 2 positions became available at one of the local hospitals In NICU, which is a floor I really want to work on. Even though it's a specialty floor, the job description stated that it required no experience so I applied for both positions. This particular hospital also has an RN internship(which I tried getting into last year) but I was told that I don't qualify for the program anymore because I now have more than 6 months worth of "experience" (sounds odd when all I hear is that I DON'T have enough ). Anyway, I put in my application online for both positions. My question is, should I make the next step and contact the nurse manager of the floor just to kind of introduce myself and show that I'm really interested in this job? I just put in the application yesterday, so I definitely wouldn't be doing this until next week sometime. A few nurses that work/have worked at this hospital have told me it would be a good idea to contact the nurse manager because the HR department there is terrible and they don't always forward applications. I've always gotten mixed reviews on whether this is a good idea or not. I know competition is tough right now with so many people out of work, but I want to stand out from the crowd without over stepping my boundaries. Any advice on what I should do??