Can slicer vibration affect thin-slice accuracy?

Yes. An unbalanced blade, worn shaft bearings or a jerky feed drive will shift the cutting point cyclically, and the thinner the slice, the larger that same amplitude becomes relative to target thickness. Insist on a trial at production speed with your actual product, and separately check blade balance, locking flange and base isolation. During acceptance, log vibration amplitude alongside thickness spread over a continuous run to see whether mechanical movement has turned into out-of-tolerance slices; motor current fluctuation is worth capturing too, and all three sets should go into the factory test report defining the machine's thin-slice capability.