Does sampling ~> Nyquist frequency capture harmonics?
This is called "aliasing" and it is simply a result of periodicity of sine.

$\sin ak$ = $\sin (a+2b\pi)k$ (for integers $k$,$b$ - $k$ being the sample index)

So, if you maybe have $a=1.3\pi$, you could also see it as a signal at $-0.7\pi$ (a signal of negative phase at $0.7\pi$), or rather: you will not see any difference in the samples.