These systems are designed to work at around one Bar of pressure but, as you've discovered, they will actually operate at less than this. One Bar isn't very much most domestic water supplies produce at least 3 Bar in static pressure.
With only a tiny bit of pressure in it, there is a possibility that parts of the system (behind the pump) might go into negative pressure, which would mean that air could get drawn into the system from the pressure relief valve (depending where it is located in the system). Also you put strain on the pressure controlling rubber diaphragm that sits itside the big metal balloon-thingy (techncal term) because it will be permanently squashed into one side the metal cavity. When that starts leaking you will curse and have to call out a plumber to fit another one.
So there's really no reason not to run it at less than 1 Bar.
It does not control the rate at which the rads heat up.