How important is it to submit papers early to a conference?
With a typical peer-reviewed conference, submission number has absolutely no effect on the way a paper is treated.  Lots of excellent well-established folks submit at the last minute, and paper assignment is generally not done until the deadline is passed.  Furthermore, paper assignment is often done with the assistance of a paper-handling system like EasyChair, which includes randomization and non-order-based heuristics.