Online applications: status meaning and what to expect?

I've applied to several associate level positions at a few bulge bracket banks using their online job search and application features. In each case, I named a reference at the bank and/or had a contact at the bank personally follow-up on my application. It's been a week and my status is remained "Submitted" for each position. Is this a good sign, a bad sign, or does it mean nothing? How long does it usually take to hear back about these things? Or is it possible I'll simply never hear back? Thanks!