Gavin
IUCN classification affects the wild population only. Sometimes governments will enact legislation to further protect the wild population that may result in some changes in the animals native area/country however given that the best possibility for the conservation of species in this situation is captive breeding i doubt even this would occur.
Also on a related topic the IUCN red list is largely unable to accuarately classify aquatic creatures as it is designed to suit the life histories slow breeding terrestrial creature with average selective pressure and charateristically long generation times.
Animals that produce the number of young that salamanders do and appear to be density dependant (assumption based upon cannabalism and life history, please feel free to correct) will have a much more limited genetic stock per number of mature females, also they have the potential to move alot further and have a larger potential niche (obviousely limited by human activity in this case). Due to these factors among others if the IUCN red list was suited to the species it should have been listed as critically endangered a long time before now. Alos the list has only evaluated less than 1% of the earths species, fair enough it looks at the ones assumed endangered first, but this is still very low and very few aquatic species have yet been evaluated. Furthermore of all the evalauted species the listing has only appeared to aid around 3 or 4 so it is not a very efficient method of protection.
From this you would assume that if the mexican government were to behave responsibly they would give little thought to the IUCN status and more thought to conservation efforts regardless of the Status. So in a word "no" changing the status will not effect breeders and pet owners around the world.