I think in nature toes that are missing due to an accident or injury could affect the ability of a bird to find a mate because there are plenty of other potential mates with all their toes. Kind of "survival of the fittest" type thing. In captivity, since there is usually not a large pool of potential mates to pair up with, it probably doesn't make as big of a difference.
Congenital defects probably can affect fertility, as the missing toes are likely just an outward sign of a bigger genetic issue. I don't think genetic diseases are studied much, if at all in parrots, so I doubt anyone knows what 57 disorders missing toes could be linked to and how to test for those disorders and figure out which ones affect fertility. Heck, they barely understand genetic diseases in humans...