Networking help

I am completing an online RN to BSN program. I decided to go back to school after applying for several months with no calls to interview despite experience. I live in a large metro area but I've heard it is competitive here, and so far I haven't had any opportunities to even interview. Is it possible to network with nurses in my online class? There are nurse managers and floor nurses in the class that actually work in the area, but I realize they are there to learn not be solicited by someone needing a job.
What makes you say that? How do you know they aren't keeping their eyes and ears open for nurses who also cared enough to improve their education? Go for it!

Thanks GrnTea. Any suggestions for how I should go about it? Ask directly?

Of course. How else? "Hi, I'm in your research class, and I heard you were a med/surg floor manager at ABC General. I've always wanted to learn more about cardiopulmonary and would like to know if you would consider me for your next vacancy. Oh, you have a vacancy now? Excellent. Here's my card; can I email you my resume? Who should I ask for in HR when I apply? Can I use your name? Thanks so much! How was that last exam for you?"