It depends on the no-kill shelter. If it's a kitten, as this one is,
some no-kill shelters will take them. Some won't, of course :


It is true that some nonprofit shelters (I really don't like the term
non-kill, which is undefined at best and misleading at worst) will take
underage kittens or unsocialized small kittens into foster care if they
have such a program. Some conventional (city and county) shelters will
take such kittens into foster care for that matter, City of Seattle among
them. I seem to recall the kitten in question was at least a juvenile,
though. The nonprofits won't take an older kitten because they have a
choice, and the conventional shelters take them because they must and then
euthanize.

Sharon Talbert
Friends of Campus Cats