even if the parents are registered, the puppies would not be registerable, they would be mutts.
i HIGHLY disagree with the purposely mixing of 2-3 dog breeds (aka designer dogs).
why do you want a "morkie"? why not just get a yorkie or maltese? why not just get a tiny mixed breed from a shelter or rescue? you'll pay much less. most likely, if you buy a "morkie" it won't be well bred. the people who breed these mixes are most likely just looking to make $$$. the reason good breeders breed is to improve the breed. most don't make any money (some lose money) between vet bills, time, food, health testing, shots, etc.
since, pretty much all of those designer mutts are badly bred and come from puppy mills, they'll be prone to health problems, so look forward to lots of vet bills.
no matter how cute those puppies look, you could find an equally or cuter puppy by looking at shelters. there are lots of chi-a-poos, morkies, labradoodles, poochons, puggles, etc in shelters that need homes or else they'll be killed, why not help them??
if you do decide on a purebred yorkie or maltese, i would be more than happy to help you find a great breeder.