As a former hiring manager, you have no idea how crazy that can get. Job openings draw tons of applicants, and it can be overwhelming. I will tell you I have DEFINITELY hired people that followed up. It showed they had initiative and really wanted the job. Obviously that wasn't my only criteria, but if they met the other qualifications the fact that they followed up was a strong point in their favor.
"A mistake is not failure but feedback. -Rod Gilbert"