So that means if the pressure discharge piping is close to zero, then the discharge pressure of the recip pump will be close to zero? If so, how can the discharge pressure build up at the discharge?
Yes, discharge pressure would be close to zero. It doesn't build up. It just moves the fluid out of the pump into a void. If there's a really low discharge pressure the check valve might not close properly if you have a piston type pump but screw or progressive cavity pumps will work at zero discharge press uresas they don't have check valves.
I knew it wouldn't be that easy....
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
Normally, I say NORMALLY you do not need a Check Valve for a Reciprocating pump or a Diaphram Pump. These pumps by their design are in fact a check valve.
The OP is talking about recip and diaphragm ( AOD). The suction pressure has no effect on the discharge pressure for recip and AOD. The suction and discharge check valve is part of the pump.