To harmonize above posts #38 through #45 (excluding #39 and #41):
A tire (within its stated range of inflation pressure) is of course more compressible than the wheel on which the tire is mounted, by many orders of magnitude, but to conclude that the wheel has no effect on suspension (e.g., handling, comfort, etc.) is to ignore the interaction between the wheel and frame. The frame and the fork also function as components of the suspension, and even if you replace one wheel with another wheel which is exactly as stiff but weighs more or less, that affects how the suspension works because it affects attenuation.