Not exactly. If a closed loop goes up and down the pressure head cancels as you point out, but that is just one consideration. Here are two others:
- There are 'frictional' losses in a piping system. These frictional losses don't cancel out like pressure head. The longer the pipe, and the more restrictions in it, the more pressure loss there will be for any given flow rate.
- There is also a problem with elevation changes in a pipe system. If the pressure in the piping system drops below the 'saturation pressure' of the fluid, the liquid will begin to flash or boil.
So given any piping circuit, there will be a pressure loss which increases with flow rate, and when designed the piping system must also not change phase without care being taken to accomodate that phase change.
One other point to note is that there are fundamentally different types of pumps which can be broken down into two catagories, positive displacement and what is sometimes called a rotodynamic pump (ie: a centrifugal or similar). A positive displacement pump puts out a given quantity of liquid regardless of pressure, as long as it has the power of course. A rotodynamic pump or centrifugal pump puts out a flow rate which is dependant on the difference in pressure between the inlet and outlet. So for any given closed loop system, you can change a restriction in the system to give you more or less pressure restriction, and the constant displacement pump won't change flow, but the centrifugal pump will.