Good one mnfish. This was one fish I was equally curious about. Jury is still out, officially, though Travis (CJBS2003) had this to say about them:
I do not have any experience with central mudminnows but have a lot of experience with eastern mudminnows which both are closely related. It's been my experience that mudminnows if given reasonable amounts of cover(vegetation) are quite predation resistant. I have seen them remain in ponds even with high LMB numbers. From my experience with them in aquaria, they're very shy reclusive fish. They stay in cover until darkness when they will emerge. So they seem to be nocturnal in behavior. Since YP are not nocturnal, they may or may not be a good pray for them depending on how you look at it. Mudminnows are most closely related to pike and pickerel. They actually have a fairly large mouth. Just how much competition they would be for YP and BG, I am not certain. I never see them in large numbers no matter what the habitat is or the fish community. They do seem to do better in suboptimal habitats where larger predatory fish are less common. I don't put them at the top of my must have list.