No, hiring organizations will not see how many applications you have submitted, or to which organizations. Remember, the hiring organizations do see your complete candidate profile, including work history, education and your impact statement.
Effective February 13, 2015, you are able to upload a unique cover letter, references, writing sample etc. for each job application. For each job you apply to, you are able to upload documents, including a cover letter, tailored for each specific job. The hiring manager for each job will only be able to view the additional documents you uploaded for that specific job.