Yeah, it definitely varies. With the hospital I'm at now, I had submitted the application about 3 months before I got a call, but they didn't have any RN jobs posted either. The opening I filled was one of two that had just opened within a couple weeks of when I got the call. Two hospitals called me within about 2 wks of applying & I had one large hospital call me the day after I applied online! In that case, the nurse manager for the unit said she preferred to review applications herself; otherwise, it typically would be weeks before HR ever forwarded any to her & if she has openings, she "needs to fill them ASAP!"
Also be prepared to wait even after being offered a position. The larger hospital I mentioned above would have had a start date about 6 wks after the interview! Where I'm at now, I was able to start the following week at similar pay & it was closer to home.