I suppose its possible with a low quality CRT that has poor construction, leaving loose parts or thin plastic fins that can vibrate at harmonics of a lower frequency, but high quality CRTs don't have this issue.

Extra or louder noise does not occur in normal operation of a correctly functioning flyback transformer circuit. Any frequency or harmonic (vibration) that occurs that is not the specified frequency of operation of the flyback transformer is caused by a problem in the circuit. A brand new CRT with known good parts will not have any kind of extra harmonic.

I had to replace a flyback transformer because it was too loud, and it was a pretty simple job. Hardest part was finding a new flyback transformer. After replacement, the noise volume was reduced to normal levels.