It appears to be a direct acting valve you have. A DAC has a spring loaded disc that rises under pressure only if the water has enough pressure to overcome the spring pressure. My vote is no in the way of you being able to adjust your water pressure for your new pump. My thoughts are that if it was installed from the factory backward; the only way I can see water passing through is the spring was backed off enough to let water pass backward.
I just have to ask why there is a pressure regulator beyond your water pump. I can see one needed for a city water hookup but the factory put it too far down the line if your pump has to fight it too. I think it could be removed all together and either relocated or placed to use when bypassing the pump.
With that, I don’t know that I have been able to identify every water line in the picture. Does the regulator supply the whole coach with water or only a faucet(s)? What is the red valve that is closed? And the biggest question I have is that a check valve underneath the the regualtor? If so, it appears to be facing downward too? If Im looking at the check valve correctly, is the regulator really backward? The coach would have no water if the check valve is working properly.