Hydraulic pump converts mechanical energy of prime mover into hydraulic energy for system use. Hydraulic energy is the combination of pressure and flow required by the actuator to perform useful work. It's important to understand that hydraulic energy is both pressure and flow, because one can't complete the work without the other. The pressure is made up of trapped fluid and the flow will have no energy to move the fluid alone.
The transmission of force is indeed synonymous with hydraulic pressure, and it is also the basis of kosford's law, which points out that "when pressure makes it disappear, flow is the rate at which pressure can be generated." For fluid movement, the pressure reaches the pump position; always. It is wrong to face the fallacy that pressure is against flow. The pressure will rise to the pressure required to overcome the downstream resistance, but if the pressure does not start at the pump, the flow will move backward.
The pressure in hydraulic pressure is the result of Newton's third law of motion, which makes every action have equal and opposite reaction force. The reverse force can be loaded by the cylinder or the flow controller, while the pump doesn't care.
It will continue to push the fluid as the pressure increases to overcome the resistance, even if it causes the prime mover to overload.