There are many things a VFD can do to cause vibrations in the load.
It mainly comes down to the waveshape of the current applied to the motor windings. Purely sinusoidal currents will cause no more vibration than across the line operation, however, there are also other considerations.
For example, let us assume your mechanical load has a resonant vibration when it is run at the equivalent of 3Hz. When the VFD runs the load at this speed, the vibrations have the opportunity to "multiply" very much like Ella Fitzgerald's glass in the famous "Is it live or is it Memorex?" commercials. This assumes the VFD output is sinusoidal at 3Hz.
If your drive is exciting the motor at one of its resonant frequencies, then you need to implement a "band skip" function which bypasses the known bad frequencies. In the above example, I'd probably put in a band skip from about 1.5 to 5 Hz and see if it helped. The drive will typically still excite the motor in the "skipped band," but will either operate continuously above or below the skipped band, going through the skip as quickly as possible according to ramp parameters.
If the applied waveform is NOT sinusoidal, then it will excite the motor/load in such a way as to cause additional vibrations resonant with the harmonics causing the non-sinusoidal waveforms. Older VFD systems that had the notorious "six-step" outputs had harmonic noises at the 5th and 7th (and 11th, and 13th, and all odd harmonics not divisible by 3). These harmonics were present on the VFD output, and filters could only account for "so much" of this distortion.
The worst case is when you have an electrical harmonic (causing vibrations) that corresponds to a mechanical resonance (multiplying the vibrations). When this occurs, I've seen Bentley Nevada vibration monitors practically pick up a telephone to dial 911. You would swear the floor is about to collapse.
So, the answer to your question is "Yes."