The purpose of the check valve in the cold water input, is to stop the hot water from backing up into the cold water lines. So that you don't have hot water coming out the cold water tap when you open it.
There are two schools of thought about it. Raritan doesn't recommend installing one, because with that small of a system, the pressure builds up rather quickly as the water heats up - and the check valve doesn't permit anywhere for the water to go as it expands. Thus, the pressure relief valve on the water heater will open more frequently than is desired - unless you also add an expansion tank into the system on the hot water side.
Raritan's pressure relief valves are set to open at either 75 PSI or 210 degrees, F. Many water heaters have their pressure relief valve set to open at 150 PSI, like a household water heater. But with hose or flexible plastic tubing frequently being used for the water lines, instead of metal piping, there is a higher chance for bursting a hose or blowing out a plumbing fitting if the pressure on the hot water side were to exceed 75 PSI.