If you're talking about the mechanical design of the heat exchanger as per ASME Section VIII, the answer is yes. At the very least you need to know the fluid density in order to account for the hydrostatic loads.
Additionally having all of the process fluid characteristics is important for specifying the appropriate TEMA configuration, selecting the appropriate construction materials, setting the appropriate tube pattern and pitch in case external cleaning of the tubes is required, choosing an appropriate corrosion allowance, specifying the appropriate tube-to-tubesheet joints, and selecting the appropriate gasket material.
-Christine