Electrolysis of Beer
It's hard to say what exactly you would end up with, but it probably wouldn't much resemble beer. The trick with electrochemistry is that a lot of things are electroactive and what reactions actually occur in a given reaction are not always easy to predict and depend on electrodes, solution composition, pH, applied potential, etc. Depending on your electrodes, ethanol may be significantly more easily oxidized than water. A quick literature search shows that platinum and gold are both decent catalysts for ethanol oxidation (platinum is commonly used in fuel cells for this reason), but even with other materials, I can't imagine any conditions in which one could easily enrich an ethanol/water solution in this way. Many organic compounds, probably including some that impart flavour, are likely to be oxidized as well, even if the ethanol wasn't, so it would certainly affect the taste.

Additionally, the electrolysis of water requires a large amount of energy, far more than distillation, so even if it would work, it would be an expensive way of doing it.