I've never submitted to a "here's my info, hire me!" site (and wouldn't), but I have filled out several job applications via browser and it was hosted by the place I was applying to. Having filled out the same application on paper when I was first hired, I can say the online is MUCH better
BUT... I think the cover letter is your first intro, a "do I even bother opening this app and reading the resume" type thing. Express your interest in working in your field with THAT employer, and why (they are the best, next step in career, location change, etc).
And, having served on 15 or so hiring committees (for AVPs, VPs, CISO, full time and adjunct instructors, various administrative/professional types, sysadmins, etc) I can say that HR handed us every part of every application that was submitted. I can also say that if there were more than "a few" our first cull became applications that weren't 100% complete (cover, resume, 3 letters, college transcripts - applying to a college can be intrusive!). If we couldn't get enough folks to interview after going through complete applications, we started wtih the incompletes that were only missing their transcripts, and only bothered with them if someone appeared to be REALLY good from their resume and letters. And even then we had to have transcripts before going on past a phone interview...