Some RVs have separate water hose fittings for city water and separate for tank fill. If you have one hose fitting for both like I do, you fill fresh water tank by opening the fill valve. If this valve leaks, two tings will happen:...your fresh water tank will keep filling as long as you are connected to city water and...the water pump will keep running intermittently circulating water from tank back into the tank depending how bad is the leak.
Installing the check valve between the pump and the tank will have one big side benefit. It will PREVENT the content of your fresh water tank ending up in your carpet if there is a leak in your pump or strainer. The check valves have the property called "cracking pressure" which is a pressure required for the valve to open. This pressure is around 1 PSI or slightly more depending on type. One PSI is a pressure of a water column 27.7 inches high. So if the water in the tank is 27.7 inches high or less, the valve will not open and it will hold the water in the tank.