Unlikely. The BBC would be very daft to run an open-signup server. And a closed-signup server would only have the problems that BBC employees themselves bring.
There's a whole long standing organization of sysops dedicated to silencing and blocking the (few, I've never even heard of one myself) places on the WWW that the sort of stuff that you are talking about would come from. If the BBC sysops are on the ball, they'll already be looking at what block lists to subscribe to.
In fact, they've had the system up since June, and I wouldn't be surprised that they haven't already been importing blocklists. Alas, the "about" page doesn't say, as it normally would, what servers are moderated. But I can understand why the BBC would not want to get into the silly game that would (and does) result if it did publish its moderation list.
It's not well publicized, and resources for new sysops being poor is one of the problems with Mastodon et al., but I hope that the BBC people are on the ball in this respect.
> There's a whole long standing organization of sysops dedicated to silencing and blocking the (few, I've never even heard of one myself) places on the WWW that the sort of stuff that you are talking about would come from.
I was thinking more along the lines of subreddit trolls, who will come in and spam shock/csam images trying to bait the mods, not actual CSAM distributors with known IPs or whatever.
The BBC will certainly attract that kind of internet denizen. They would have to have employees (or automated system) staring at their post replies constantly, watching for this kind of stuff.
The FediVerse doesn't work that way. There is no "the" mods.
The people posting this stuff won't be posting to the BBC. They will be posting to far away places each with their own moderators. They'll either get suppressed at the source, by those moderators, as complaints come in (which they will probably do quite rapidly); or it will get around that those far away places don't moderate, and the far away places will get silenced and blocked and make it onto the aforementioned lists, meaning that the (civilized) world won't pull any posts from them.
The reporting system, bear in mind, reports to the origin server, which won't be the BBC. If I, for example, see an unacceptable post in reply to something posted by the BBC, my report doesn't get seen by anyone at the BBC. It gets seen by my local sysop and the sysop of the origin node.