If you read my statement above with what i think it should be included in a choreographic work to be called a Ballet work, you'll have the answer. The way your question goes, asking about "Balanchine's Nutcracker", contains itself the concept of the whole thing, including Act II with its pointwork. So there...it already falls into the requirements for a "yes".
So ... is your point that Balanchine's Nutcracker is not ballet because of the large amounts of mime dancing in it? Even though the first act contains children's ballet dancing, which is not on pointe?
How about Fokine's Scheherazade? Is that not a ballet?
Now, on the other side, if I am presented with an isolated 3 minuts excerpt of a chunk of a bunch of little kids running around-(doesn't matter if it's Balanchine or not, Nutcracker or not)-without the rest, meaning that it would be, let's say, the "party scene excerpt from Balanchine's Nutcracker", then I really couldn't have the same answer. What about if I'm not familiar with Balanchine's kids scene...what about if someone is not familiar with the whole Nutcracker whatsoever...? At the end, it would be just that...a bunch of kids running around-(and again...maybe even it would be impossible for me to identify it as Balanchine, if I'm not told before that it is his choreography).
I have had the same trouble with things like Villella's "Nine Sinatra's Songs". I can't understand why is it called "Ballet". For me it doesn't look different at all from what I've always seen as Ballroom Dancing.
About Sheherezade, I can't really speak about, having never seen it, nor would I dare to go as far as questioning Fokine. That really goes beyond my knowledge, which, of course, is extremely limited. I'm not an expert, nor did a came with the "official" denominations of what a Ballet is vs. a Choreographic Work. In Spanish we never use the word "dancer" within the Ballet domains-(there's not even a translation for it)-so i guess that makes it simpler for us, whereas i see that sometimes here in US people talk about "Ballet Dancer" or "Ballerina" with the same meaning at times. In Cuba we call the women who dance on her toes "Bailarina", and the male who dances in a Classical Ballet Company "Bailarin". They don't belong to the same category as those who dance in other companies-(folk/contemp./modern...etc, even it they can point their toes the same)
But now I'm intrigued with Sheherezade. I will try to find Youtube clips of it-(I know there is a reconstruction in DVd done by Liepa)-to see what's going on.