In a related note, Bell's Theorem (along with a few experimental results) demonstrate that no theory of (local) hidden variables can account for quantum theory[2]. This means that the limit is not just on our ability to measure the information in an atom. It literally doesn't exist for us to measure. Quantum mechanics is confusing =P.
[1] Specifically, the information measured in binary bits is bounded by the surface area divided by four. I'm not 100% sure what the unit of surface area is, but I believe it's Plank units.
If space-time does turn out the be physically discrete at the planck length, and the limits of our measurements are actually reflecting the universe's true discontinuous nature, then this would imply that there would be a limit to how much state you could push into an atom.
Any real physicists please feel free to shoot me down in flames here. This is just my (plainly) limited understanding of the situation.
Perhaps the confusion comes from the fact that the easiest way to prove a formalized process is Turing complete is to express a simulation of a Turing machine.
I must admit that since HTML+CSS3 requires clicks (at least in this implementation), I don't consider it to be really proven to be touring complete.