Nontransponding traffic is totally baffling on the occasions when it is visually identified and quite obviously it is a new-ish type plane which will obviously be carrying a transponder.
That some people fly with the TXP switched off, allegedly to avoid getting busted for a CAS bust, would be utterly stupid and an appalling testament to the "quality" of PPL training which is still teaching WW2 (no, actually WW1) nav techniques and no GPS.
Unless, following the bust, one flies back home at a pretty low level, there will be a radar track left somewhere, enough to follow if one has made a real exhibition of oneself and the motivation is there. What they probably cannot then establish is which plane based at that airfield did it, because the records are usually a bit slack. But having Mode C on is not going to affect that. Mode S would allow the plane to be traced by the 24 bit code, assuming it has been correctly configured.
But the CAA rarely prosecutes CAS busts. They seem to go after high public profile stuff like airshow TRA busts (like that bloke from Belgium who got done a few k for busting the Eastbourne show). To get prosecuted for a CAS bust, you would need to bring down Heathrow, and then tell the interviewer that the UK is a free country and you are allowed to do this.
I've done the survey. Mode S always on. It has to be said however that for the CAS bust context, Mode C is just as good.