Ok so I tried this now in a quick test with the YN 560III. Somehow it doesn't work as I described above. Synchronizing Pixelshift and flash wasn't possible. The four exposures seem to be in an irregular sequence instead of exactly 1/4 of the total time each. There are always one or more frames that are un-exposed or only partly flashed.
However, what works is setting a long exposure and trigger the flash manually by hand. For example: 1.5 second exposures are manageable. Press the shutter and then trigger the flash four times. The display shows the sequence of the four images taken in real-time. This helps to get the timing right.
But: The flash brightness needs to be _exactly_ the same. Otherwise the colours will be off. If one of the frames is brighter or darker, then this will be visible as a colour cast. For example, a brighter capture of the red-pixel-frame will be clearly visible as red-ish cast in white areas.
Motion detection kills these artifacts but then the PS benefit is also gone since it affects the entire image.
I want to try it in more detail with studio strobes, but for now it looks like continuous lighting will be the way to go.
(And coming from the K-5iis, I learned that PS isn't something to hammer away one frame after the other. A 32GB card will fill up rather swiftly...)