Sure, and those schools should have those children cater weddings and other events since many of them are probably exceptionally gifted at culinary arts.
Really, though, the answer is a big YES. Gifted children suffer where there is little to no stimulation. Ever see the movie by Jodie Foster titled, "Little Man Tate" ?
I recommend it if not. I agree 1000% with the portrayal. Kids, like adults, wish to flock with the feather of their kind. Not to knock other children, but their self-esteem suffers, too, when the majority singles them out due to their giftedness.
In the presence of mediocrity, precocious children are often alienated from those who can endure mundane activities, even normal playing with toys and sporting goods that are granted to them... this, too, is portrayed in LMT.
That Foster is a Yale grad with a Literature degree, leaves her with some room to make the statement the movie makes. Yale Literary Schools are brutal and thick!!! You can even watch the classes online on YOUTUBE - believe me, it is a GREAT free education!!! Go for it and try.
That aside, schools for the gifted only add to the dimensions of their gifts. Growth requires water, food and light. Plants and humans need light to live, and figuratively, gifted children need to see their own light reflected in other, like-minded quirky nerds so they don't go on in life turning their genius into recklessness ... this, too, has been documented. Deviants are often the most brilliant. They deviate because the status quo is to them, in need of change, ergo - they become that change often to the effect that they martyr themselves in one form or another; usually to their own dismays, this unfortunate probability occurs. If you know about Wilfred Bion, then you probably know well that the genius cannot endure the "Basic Assumption Group." Regarding group dynamics, it may be difficult to tell if the gifted deviant isolates himself from the group, or if the group has shunned him for his brilliance - a brilliance the group and its members, simply CANNOT reflect.
There are millions of reasons for what you're onto here pertaining to these children. Sad to say it, but some of these kids are the first to suffer from environmentally induced dissociative disorders, and if ill-regarded for their capacity, will or may seek drastic means to be heard. They are self aware, and that alone is scary... they know what they could offer, if only the proper domain was provided to do so.