This question has been asked in several different forms, and the answer given seems to be always "no" because we can "simply read off the yield curve". However, since the yield curve (or "a yield curve" in a multi-curve world) is constructed from various market instruments (e.g. futures), do we not need a model for rates to derive the yield curve from these instrument (to, for example, calculate a convexity adjustment to be applied to futures)? SO, the question is, given prices of market-observables instruments. do we need a model for dynamics of rates to price a vanilla IR swap?
The answer is that it depends of the Zero Curve you're looking to build and the precision and maturity of it. For example, for the Libor3M curve, you might need indeed to use futures if you want to obtain a clean smooth curve for maturites close to 1Y. But again, if you're planing on using longer contracts, you can just bootstrap that part of the curve. It depends the level of precision you're looking for respect to the market.
Most of the time, curves are built different from each other, so you just need to understand the Index you're trading. So the answer would be, yes we need a model for dynamics of rates, as long as the index underlying the swap has the instruments to obtain such data. Otherwise, you won't be marking to market.