Planes can and do sometimes fly over China.
However most planes don't fly over China because there's not as many airways or airports over central China but there are some planes that do make flights over China when needed.
A plane also needs approval most times to fly over China because of threats that China believes could be happening from the USA to China and vise versa.
But if the airline is approved to fly over China then they can and do so.
India and China do not have frequent flights between them though either.
But planes do fly over China more frequently than most people think.
You could not however just fly your own airplane from USA to China without approval or fear being shot down due to security reasons.