How to follow up on an on line application?

I have a question and could use some help. Now that just about everyone uses the computer for applications in my area, I am confused. Is there an appropriate way to 'follow up'? Do you send an email? Do you call? The vast majority of the places I have applied have a disclaimer that comes up and says, to the effect of : We thank you for your application and rest assured, you will be contacted if we want to follow up with you.

Basically they are saying, don't call us, we will call you.

I can't seem to find a job, and now I am wondering, SHOULD I just go ahead and give them a follow up call anyhow? Or will that make me look like I can't read? (for those who's site said not to call).

I realize there is a high volume of applicants for nursing jobs in my area, so they have their pick, and that is great for them. I just don't want to miss out on an opportunity because I did not call and have it look like I am not interested in the position.

Thanks for your ideas and thoughts!
Wow I came on here just now to post EXACTLY what you have posted. I'm from the philadelphia area and it is really really hard to find a job right now as a new graduate RN. The last time I was applying for a job they still used paper applications, where you physically handed it to someone and you could go home confident that they received your application. I have a really big issue with this online nonsense because I feel as though I'm just filling out a survey, pasting my resume into a box and sending it into a virtual abyss, not knowing if the hospital even received it. And then they have an automatic message come up saying not to contact them or email them back. How are we supposed to know that we did everything in our power to assure they recieved our application if we can't follow up on it? I havent called or emailed anyone after sending it, but I havent heard back from numerous places so I'm considering the email option. I'll just say that I haven't heard from them and was wondering if they received my application. I mean, it doesnt get any worse than not hearing back at all, so what harm can a little innocent email do? right? :typing
Call HR and ask them if there are any applicant surveys that need to be filled out after the submission of an online application.The call could go like this: " Hello I'm, X, I just submitted my online application for, X position. I am calling to inquire if there are any follow up surveys for me to complete, or if there is anything else that I need to do to complete the application process? " Now be silent and force them to answer you!You could also ask if it is appropriate to turn in a paper resume (and at this point is when you staple your letters of recommendation to the back of it.)Good luck.I have always found that being aggressive has landed me the job.