Other than it potentially being a big waste of your time, it can't hurt to apply early. However, as someone who has been looking for that first RN job for several months beginning before graduation, no one is too interested in you until you have your license, if at all. They don't need to "pull them in early", there are plenty of quality, experienced RN's to choose from without even bothering with the new grads. And for the few new grad jobs there are, the competition is fierce and the hospitals have their pick of the litter.
I don't mean to be a downer, and I believe things will change in the near future, but I thought you might want a different perspective from someone who is were you will be in 6 months. And, maybe things in your part of the country are different. But, if it was me, I wouldn't spend too much time applying for jobs right now. It is very time consuming and your time would be better spent on your studies.
I do recommend though, as someone else mentioned, to use those clinical opportunities to network and show off your personality and work ethic. Get to know the nurses, try to meet a manager, etc. See if your preceptor will write a letter of recommendation for you and ask if you can use them as a reference when you apply. When your at a clinical, assume you are "trying out" for a position. You never know who is watching you. For now and probably in 6 months you are likely going to get that job by a connection you have somewhere.