It depends on the type of system. A system such as you described would provide hydraulic pressure all the time but when you were not actually using the hydraulics, the engine would still be under load pressurizing the system to the pressure set by that relief valve.
Most systems are open center. In those systems, the hydraulic fluid flows with little restriction through the pump and the open center of any control valves and back to the sump. When the hydraulics are needed, the valve diverts the supply side of this flow to one side of a hydraulic cylinder or motor, the pressure builds, the cylinder or motor moves and work is accomplished. At the same time the control valve connects the other side of the cylinder/motor to the return line to receive the fluid displaced by the moving cylinder/motor. Each of these valves has a safety valve in it that will connect the input from the pump directly to the output and bypass the load if the cylinder or motor is overloaded or at the end of it's travel. This type system only places a load on the power source when the hydraulics are actually being used.
As an example, my tractor has 3 safeties on it. The first is on the loader valve. The next thing in line is the diverter or flow divider valve that sends fluid to the steering system or 3PH as needed. That diverter has a safety on the steering circuit that returns directly to the resovoir if I should overload the steering cylinder. From the flow diverter the main fluid flow is back to the 3PH valve which in the lower or neutral position flows directly back into the resovoir tank. There is a safety in that valve assembly that flows back to the resovoir if the 3PH lift limit is exceeded when the valve is in the lift or neutral(hold) position. In my system, the first thing after the pump are the quick connects that connect the input and output of the loader spool valve. As stated, if you disconnect these, this blocks the flow completly. On a completely blocked flow without a safety bypass to the resovoir, that pressure will find a "non-standard" route to vent itself or will stall the powerplant.