Any stable enough virtual reality, as seen from inside, makes Godel and Heisenberg inescapable, imo. To make Godel and/or Heisenberg false would probably need infinite trickery from the virtual reality administrator.
I am willing to bet that most of the *quantum* weirdness is a consequence of the already virtual character of the possible realities consistent with our digitalness.
If *you* are supported by a virtual reality, and if you have the time and the space to do any conceivable experiments on your apparent neighborhood, you will discover that your reality is virtual. Only if both you and the virtual reality are updated each time you find a "logical" discrepancy, you will not been able to infer the virtuality. But then you are in a Harry Potter like structure which will need some super-observer-administrator to trick you perpetually. That would be a "malicious God"! And actually even if such malicious God exists, I don't know how he will make you remaining, from your point view, in that tricky reality, given that it will be more probable from your point of view to continue on some normal extensions.
Assuming comp, a virtual reality built for making you believe that you are in some "real reality" is bounded to fail statistically, for the same reason that you cannot probabilistically *remain* in a Harry Potter like situation.
The science-fiction book "SIMULACRON III", by Daniel B Galouye, does illustrate the point that we *can* discover we are virtual or dreaming, by finding logical discrepancies. Actually the "lucid dreaming" phenomenon could be seen as a natural illustration of this. (SIMULACRON III has also been made into a movie: "the thirteen floor").