Of course it is falsifiable. If you can't specify in what way you recover physics from your simulation and what computation actually occurs in your simulation then, apart from the word "simulation" making no sense, you don't have any theory to either formulate or test at all. There, falsified for you. In particular cellular automata fit that description. It has been beaten to death since the 80's and leads nowhere, unless of course anybody counts Wolfram a (new kind of) scientist.

Same problem we have in quantum gravity. We just can't recover known physics from anything at all, any combination of theories at all it seems. That includes all known instances of computation, it just blows up.

Also, Church-Turing has nothing to do with basic problems here, in particular because eventual simulating computation would be unlike computation we know (which again, makes the word lose any meaning here).