Can the heart pump without the brain?
The human heart can pump without signals from the brain. The reason for this is the structure of our hearts. Our hearts contain their own pacemakers, which send out the signals to contract.
Each of the four pacemakers can send out the signal to contract by itself. The frequency at which they fire does vary between them though. The SA node is more frequent than the AV node, which is more frequent than the bundle of His, which in turn is more frequent than the purkinje fibers.
Because of this higher frequency the signals from the SA node override the signals from the other three. If the SA node would somehow fail to either fire or transmit the signals, a takeover by the AV node would take place. This is generally surviveable for a human, albeit with a slower blood flow.
The frequency of the AV node is generally around 100 beats a minute, which gets inhibited by the nervous system. The AV node has around 40-60 beats a minute. The bundles of His would beat at 30-40 beats a minute and the purkinje fibers would make the heart beat at even lower frequencies than the bundles of His.
All of these systems are within the heart itself and without direct control from the brain. This means that the heart could beat without the brain.