Nicki, if it were me and I was wanting to use my PC I would probably use the screwdriver, turn it to the on position and turn the other two valves appropriately as show in the manual to use the system. I would hook up to the external water hose, turn it on very slightly and just see if it leaked. You might be surprised that the part that popped off is the control handle and just a secondary retention "O" ring. I don't know and can't tell from the pictures. In any event, I would sure give it a try.
If it does leak slightly, I would then dry it off absolutely completely and wrap it with something like EZ Fuse Tape (Walmart, Lowes, HD, etc.). Water pressure in an RV should never be over 40 psi due to the regulators we all hopefully use on our water hoses and the water pump in the rigs won't exceed that normally either. In any event, I would try it and see. I would not be surprised if it did not leak once opened. Who knows without trying? Once the tape anneals it is pretty tough waterproof stuff. You can always cut it off with a knife when you want to remove it.
Paul