I don't have the numbers per se for Linkedin but I can image that the number of applicants through the network increases everyday. I've recently finished Dan Miller's book "48 Days to The Work You Love" I believe he mentioned something along the lines of 8 out of 100 applicants get hired through online means whether it's Linkedin, Craigslist etc..

Usually once the job hits the general public 9 times out of 10 the position is close to being filled. Companies I believe have to receive a certain amount of applicants before they make a decision. (My guess is to rule out discrimination)

Hope this helps a little.