It would only make no difference if the result of the trial would be independent of the additional evidence that a surveillance state could in principle collect. But this would mean that the surveillance state is not necessary.
(a) Someone who has committed a crime
(b) Someone who was convicted of a crime he may or may not have committed
I was using (a). If you are using (b) then I understand where you're coming from. But I think it's not a good idea to use (b) because that would make everyone who is the victim of a miscarriage of justice a criminal when in fact they are not.
I watched an excellent speech of a law professor giving examples of people who broke the law without realising. Unfortunately, I don't remember how to find that video.
My point is that law makers define what a crime is. The effectiveness of law enforcement doesn't change that fact. It's not good to have laws on the statute book that wouldn't be there if only they could be enforced.
So if the surveillance state highlights the fact that we're all criminals, what that should tell us is that criminal law is in urgent need of a root and branch review.
The surveillance state is a very bad idea for many reasons. But saying that we reject the surveillance state because then laws could actually be enforced is a questionable argument. There are many better ones.
Odds are, in a few hundred years, we'll end up right back where we started.