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Streaming potential is an electrochemical phenomenon that a that relates electric currents with the relative movement of solid and liquid phases in contact with each other.

So when a liquid moves past a solid a potential is generated. The equations for the values of the potential and current generated can be found in this Wikipedia article. My question is, is the reverse true? If I applied an electrical potential difference (instead of applying a pressure difference), would a pressure difference be generated?

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Your assumption is correct. Electrokinetic pumps use a potential difference across an osmotic membrane, i.e. through narrow channels, the inverse of flow causing a streaming potential difference. There are other aspects of the phenomena such as electrophoresis, capillary osmosis etc.; see:

Electrokinetic Phenomena a

On the Efficiency of Electrokinetic Pumping...

and

short video demo

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