I don't entirely see how you can simultaneously argue that 'you do it when there are not many people on' and 'there are a huge number of groups doing this'.

It doesn't seem that unlikely. "Huge" is relative, of course. But if there's a significant downtime, it doesn't seem that difficult to coordinate. Drafts take a solid 15+ minutes, and that's not going to time for every pick as everyone discusses their choices. If a group jumps on together, it means the draft is likely firing within about 30 seconds of the latest one at most, so beginning one doesn't take up that much time. So even if there are 100 groups trying to do this, chances of them not being in a draft and coordinated to jump in a pod at the same time seems low.

I know that from experience. Back before leagues were a thing, I did a few fan group drafts just like that. We had little trouble and tended to have at most one person who wasn't part of the group playing. And that tended to be at more 'peak' hours, like 5-10 PM in North America.