no, natural harmonics are always integer multiples of the frequencies which you already hear. so you might be missing out on some higher harmonics but they only go up from the base frequency.
the "noise" occurs when those harmonics are aliased -- meaning that the sampling frequency of the A/D converter (usually around 14.4 kHz, correct?) isn't sufficient to capture frequencies higher than ~7 kHz and aliases them to some lower frequency which manifests within the audible range. this might be what your friend was referring to.
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