Generally speaking, structure prediction programs look only at the thermodynamic minimum, without consideration of the kinetic trajectory of folding.
The main reason for this is mostly time considerations. It's very difficult to accurately model the true folding pathway of even a moderately sized protein. With special tricks and a bunch of computing power, we're barely able to simulate a folding trajectory of small, simple proteins. We aren't (yet) able to do so with anything of reasonable size.
Instead, what protein structure prediction programs do is take a shortcut, skip the physically-realistic folding simulation, and instead look for low energy models, with the assumption that these low energy states will look like the natively folded proteins.
(One such program I'm familiar with - Rosetta - effectively takes small backbone structures already seen in crystallized proteins, stitches them together and asks if that looks like a reasonable structure for the sequence. If not, it tweaks which backbone fragments it uses, repeating until it gets something it thinks looks good.)
This assumption - that the native structure of the protein is the global energy minimum - is called Anfinsen's hypothesis. One rationale is related to Levinthal's paradox: unlike simple chemical reactions, a protein folding trajectory has too many degrees of freedom for even nature to exhaustively sample all conformations. This implies that stably folded proteins evolved with well defined "energy funnels" - that is, the energy landscape of well-folded proteins is such that the folded form is "downhill" from a large number of potential states. Since a large number of potential states need to point toward the folded form, this implies that the local minimum of energy which is the folded form is also likely the global minimum of folding.
The energy differences in protein folding also tend to be small - it's relatively easy for proteins to climb back up of local minimums and go elsewhere. Without the strong, global energy funnel to direct them toward a stable state, it's difficult to keep proteins from unfolding and refolding. This is why kinetic considerations like controlling the trajectory of folding from a ribosome, or having special chaperonins don't really work. Because chaperonins are catalysists, they change the rate of the reaction they're involved in, but not the equilibrium. Microscopic reversibility means that any protein which randomly collect enough energy can use the chaperonin to escape the dead end it was put in: it's not a one-way gate.
Now having the kinetic minimum be the thermodynamic minimum doesn't have to be the case - it's just the case for the vast majority of proteins we've seen. There are certain systems where we're pretty sure the normal folded form is in a local kinetic trap, and with time it can escape into a more stably folded version. Amyloid fibrils and prion proteins are thought to be one such instance. The normally produced version is in a low-energy kinetic minimum, but over time or through various interactions with amyloid or other prion proteins those proteins can relax into an alternative, lower energy conformation.
The keyword here for future literature searches is "kinetic trap". Some kinetic traps are very short lived (microseconds), but other may be longer.
Finally, I'll point you to the paper "The Protein Folding Problem" by Dill et al., which is a good review on the topic of protein folding.
