Regarding composers, The rules state that music can be used regardless of when it was composed. As stated
HERE.
J. Participating groups are encouraged to work with a local composer and/or musicians to write and record music for the films. It is permissible for a participating group to use pre-recorded music; however the participating group must have the rights to any music used in its film and must provide releases for all music used
Going by the above rule, a composer should at least work out the movie's theme (anytime prior to the weekend) - I suggest a dark version and a light version of it, so it can fit into whatever genre you get.
For the weekend composers, I suggest sitting in on the writing session to understand the genre, plot and pace of action (if any).
You can start on a Main Title theme, immediately. In fact, it's all a bit easier if you know there is going to be a Chase, Building Suspense, Comedic Background, Love Scene, etc, etc.
I was once asked to score a feature, without seeing the footage. The above mindset is what a film composer needs. There are "beds" (background music) and (if you know the Editor) you can do separate, isolated "Cues" or "Stingers" that can fit into those beds, but on a seperate audio track.
This year, I edited in the Cues/Stingers/Percussion hits first. Then I created a couple of thematic beds, as time allowed. For BUG COMPLEX, I went through a bunch of the coolest sounds on the Virus TI keyboard and recorded a note/chord of each onto a single 90 second recording and dumped it to the computer where I grabbed/cut them as needed during the edit. I didn't come up with themes, till after, when the picture was locked.
When I work with other teams (as the previous 2 years), I bring one or two keyboards to the editor's house and work on tracks as he edits. He lives too far away to jaunt back and forth, so I just stayed there for the weekend. It was kind of funny because I had never been to his house prior. I ended up sleeping over both years, until we got done. His wife would make us steak, eggs and biscuits, Sunday morning and we continued working into the afternoon. Pretty cool experience.