A student postulated that the sodium pump directly causes action potentials along neurons. Is this hypothesis reasonable?

No. this does not cause action potential.

Explanation:

Action potential is formed from the influx of sodium ions through the special sodiun channels call volatage gated channels.

The influx caused deoplarisation and if upto to the threshold level give action potential.

The influx of sodium and out flux at the node of Ranvier does not lead to action potential neither does hydrolysis of ATPs for its active transports process.

The sodium pump is for maintenance of electrochemical gradients with potassium for maintaining Resting Membrane Potential of the neuron.