The hydraulic (water) analogy supplies the answer, but first we have to take it seriously as the powerful metaphor that it is.
In a water pump, what happens if the "circuit" is all at high pressure, and the pump is fairly weak? In that case all locations in the pipes are "pushing" water. But our pump's small pressure causes one part to push a bit less, so water gets driven around the loop. The pump causes DIFFERENTIAL pressure: we could alter the absolute pressure in the pipes (inject or withdraw a bit of water from outside the pipes,) yet the pump will always create the same pressure-difference and the same overall pumping action.
In a real circuit, this is analogous to dumping a static charge on the whole thing. If your flashlight is charged to -10 kilovolts, then every wire will strongly attract electrons. Or charge it to +10KV so both ends of the battery are sucking electrons. But the 3V battery in that flashlight still creates the same small potential-difference, and the light bulb only sees the difference, and not the 10KV of electron attraction.
So to answer your original question... if you ground the negative terminal of a battery, then the grounded part of the circuit will neither attract nor repel charges (at zero volts wrt Earth,) and the positive terminal of the battery will be the source of all electron-pull. Or, you can reverse things by grounding the negative terminal instead. Or, connect two 1M resistors in series across the battery, and connect ground to their middle connection, so one battery terminal will be positive WRT Earth while the other is negative, so each terminal equally pushes or pulls.
See what's going on? Differential pressure (and potential difference) is a useful separate concept from absolute pressure or absolute potential. Learn to think in terms of differerences instead of absolute push/pull, and you'll have a new mental tool in your toolkit.
Circuit analogy with leather belts: in a system of belts and wheels, if we turn a drive-wheel and make the belts all start moving ...did that wheel pull on the belt, or push? Both and neither: it created a differential tension. It's irrelevant whether that leather belt was already under high tension or low: the system works the same because it only "sees" the differential.
Another water analogy: we don't care what the altitude of the dam is, we only care about the "dam head" i.e. the height of the water above the pipe at the dam base. Whether the whole dam and reservoir is near sea level, or is high in the mountains, it works the same. In similar way, potential-difference lets us ignore the actual pushes or pulls, and instead look only the pressure-diff or pumping action.
OFF TOPIC: in an airplane wing, does the higher pressure below the wing perform the job of lifting the plane? Or, is it all from the much lowwer absolute pressure above the wing? (On some forums you can get a flame-war started over this stuff!) But as above, you'll see that this is a misleading question, since the wing is actually being lifted by a pressure-difference, and basically the wing "doesn't know about" the absolute pressures.