At least in concept, the claim of motion by electrostatic force can be explained by theory. Since gravity can be conceived of and analyzed mathematically as an electromagnetic force, it is at least plausible that some form of electrostatic force might also impart a gravitational effect and make for motion without propellant. Perhaps, in a small way, space itself is affected by the new device. Warped, if you like.
If so, we may be on the cusp of a new era of advances in physics. By the end of the 19th Century, classical physics had reconciled theory and real world phenomena and experimental results, leaving only a few small areas of uncertainty. So-called black body radiation was one of those puzzles, which Einstein brilliantly explained as due to light being both a particle and a wave.
Soon that insight was extended to other forms of energy and matter. It took decades to piece together quantum mechanics, with physics becoming a creative and exciting free for all struggle to align theory and experimental results.
Einstein of course also took on the puzzle of how light could be one speed and the implications of that for the nature of space and time. Einstein even laid out how his theory of relativity could be tested experimentally during an eclipse. His theory was soon proven accurate, making for one of the greatest called shots ever.
Yet Einstein famously struggled to reconcile quantum mechanics and relativity and rejected quantum entanglement as "spooky action at a distance." Now, quantum entanglement is being developed into the next great advance in computer processing.
For another possible breakthrough in physics, take a look at Andrea Rossi's claim for a practical device that supposedly produces electricity through some form of cold fusion, or Low Energy Nuclear Reaction (LENR) as its advocates usually prefer.
In my imagination, I can see Rossi's Ecats producing electricity to power electrostatic drive engines. That would soon have us zipping about in well, flying saucers and the like. That's impossible though, right?
It depends on the circumstances. If your idea of an electrostatic drive engine is to have the electrostatic drive accelerate really small "vehicles" then sure, you can buy them right now. But you may need a microscope to see the "vehicle."
For a larger object it is hard to manage the electric field needed to suspend the object without breakdown of the air between the two sides of the electrostatic field region.
That's may be less of an issue in space, so an electrostatic hover board might be easier to build for use on the moon. Until you find out what the dust does.