When my school does an On-Demand Scrimmage, we treat it like a testing situation, and students report to the site where they would test for, say, the State test. Students who get Special Education accommodations, receive those services during the Scrimmage and our English Language Learners go with our ELL instructor.
The On Demand prompt for this Scrimmage is generally passage-based. We administer a Stand Alone passage, but that stays in the Language Arts classroom, and the writing is scored by ELA teachers and is meant to drive instruction.
In the allotted time of 90 minutes, students have a large task: they have to understand the task by looking at the rubric and instructions, read and comprehend the passage, brainstorm, draft, edit and revise. We used to have the kids go through two drafts, but now students just revise and edit on their original draft. This is nice because we, as teachers, can see that writing process a bit clearer, but it's taking a little retraining to get the kids to begin thinking about a "rough draft" as a "working draft."
How does your school handle On-Demand Writing? I've heard of some schools who practice it weekly! I feel that as long as kids are getting plenty of opportunities for quality writing instruction, those concepts will transfer to a timed situation.