Mosaic is just color, it's no different then asking if a brown tabby cat sheds more then a black cat. That being said, they do "shed" twice a year, called priming, they don't shed all the time. Even during a prime most of the fur ends up in the dust bath not all over the place. However, when scared (new person touching it and in a pet store) they will release fur as a defense, it's called fur slipping. The idea is that the predator, or in this case, new unknown human only gets fur and the chin can get away. Once the chin gets use to normal gentle handling (realizes it's not going to get hurt, grabbed, chased, poked, or eaten) and use to it's new home and you the fur slipping should stop. Most chins don't ever like to actually be held though, some get use to it but mostly you just pet them (chin and belly scratches) and let them use you as a jungle gym during playtime.
As said people tend to be allergic to the hay, dust bath, or litter shavings, not the actual chinchilla (though an allergy to the fur is possible, just uncommon). Chinchillas clean by taking baths in fine dust (which does get everywhere), so they don't have dander like a cat of dog which clean by licking.