Oh god don't read that... The transition rates for each individual state transition are drawn from an exponential distribution with a rate dependent on the ene

Oh god don't read that... The transition rates for each individual state transition are drawn from an exponential distribution with a rate dependent on the energy difference between the states. So, no, C will be visited with some probability. There are many problems with that paper, but validity of the sampling algorithm is not one of them. It is an unbiased sampler and will eventually converge to the sampled distribution (as proved in the paper). How long that convergence will take is another store. It remains unclear whether this approach converges faster than your garden-variety Markov chain and if so when and why.