One would imagine that depending on the move set used one would find very different answers to this question. To answer such questions, more realistic models with clearly defined dynamics are necessary. The move set used consists of local moves which preserve the covalent links and keep each lattice site either singly occupied or empty. This set was developed some time ago to study the dynamics of polymers. Studies involving this move set have shown that it closely reproduces the relaxation dynamics of the Rouse model.
More complex moves are possible where more than two monomers are moved simultaneously.
To correct for this, one can assign a different probability for each of the moves. We do not believe that including the possibility of concerted motions of large subsections of the polymer will change the answers to the questions asked here. In particular, it is not possible to reach the configuration in Fig. from an extended chain. The question is whether the nonergodicity of our moves will create a problem. The simple answer to this problem is that we are interested in the kinetics of folding and as long as the native state is accessible, there should no problems due to the existence of inaccessible states.