Indeed & there have been many child stars who have not been spoiled by the experience. Think of the young Harry Potter actors. Charlotte Church promoted herself at 12/13 & now, as an adult, seems totally unphased by having been the 'voice of an angel'.
It all depends on the individual child, their parents and - not to be ignored - their school.
General education is just as important as anything dramatic or musical a child or young person may do, that mustn't be forgotten.
The same applies to outstanding talent in art, sport, mathematics, even chess.
Sometimes talent needs to be nurtured from a young age but not at the expense of other experiences. Getting the balance right isn't easy but some do manage it.
I loved hearing the girl in the link singing, her voice is amazingly mature.