Hm. Well, it does prevent the thought experiment, at minimum.

If we take the rule as true, then it is incoherent to talk about a universe where the neurons in your brain are doing all the same stuff but don't give rise to consciousness. We can talk about a different structure that might be composed of neurons, but not the same structure. Whether you believe in epiphenomena or not, we take consciousness to be caused by neurons in our universe. So another universe with the same neuronal structure that followed this rule would make the thought experiment fail.

So if I have the right sort of structure of neurons and this rule, then I have consciousness. The 'epiphenomena' stops doing any work: the universe looks the same whether or not I posit the epiphenomena. So the epiphenomena isn't explaining consciousness anymore. So while the rule doesn't forbid epiphenomenal theories of consciousness per se, it does mean that if those epiphenomena are supposed to not be a causal result of the neurons in any conceivable universe, then they can't be a causal result of the neurons in this universe.