Not if you're doing short stories around a central theme, J Riff.
I'm watching the thread with interest but I'd like to see what the theme is.
Also, like TJ said, I think you'd need to decide if the collection would be "We accept anything as long as you're a Chronner" or whether you'd only accept a limited number of stories, and those of a certain quality. The second might be kind of difficult since rejection is always tough, especially from friends, but if you accept everything then you may run the risk of publishing a very uneven bunch of stories, which would make the whole project an exercise in bonding. Nice in itself but may not be what you're aiming for.
I've been an editor on academic journals and the one I worked on for longest had a policy of offering a high level of support to student contributors. If their submissions were lower quality than we published, they weren't rejected as non-student submissions would have been, but were edited and sent back to the contributor for changes/ additions etc. I've done eight or nine cycles of that for some people -- including sending various versions to anonymous reviewers (and I've been thoroughly sick of the author, and they of me, by the end of it).
Could I suggest that if you're going ahead with this, it might be worth considering making it an editing circle too? So everyone agrees not only to write a story but to edit/ critique someone else's.
Then:
(1) Everyone writes a 2000 (or so) word story and sends it to Ratsy.
(2) Ratsy sends each story to another member of the circle, who *anonymously* edits and critiques as s/he sees fit (but politely and helpfully) then sends it back to Ratsy who passes it on to the writer to make the changes (or not).
I'd suggest doing no.2 at least twice, though that's a lot of work for you, Ratsy (sorry). If you didn't make it anonymous then you'd have less work.
(3) If you had an editor or an 'editorial board' of a couple of volunteers + Ratsy, then you'd read all the stories after (2) was finished and decide if any needed more work. You could make editorial suggestions for reworking or whatever was needed.
That way you could get a set of stories of a higher level of quality, edited to standardise the grammar etc.
Whatever happens, though, we'd either need to work hard to advertise the stories etc (and potentially double the readership) or resign ourselves to the book being read only by other Chronners and possibly their mums.