So... I stumbled upon this video showing how the Anti-Shock mode works on the E-M5 Mark II and it turns out my question was based on an incorrect assumption.
This assumption is in the way a focal-plane shutter traditionally operates. As implemented on most SLR cameras, whether digital or film, after an exposure, both curtains are returned to their original positions in order to recock it for another exposure. This means the film or sensor can only be exposed in one direction of the shutter curtains' movement. In order to take a picture in live view mode, a typical DSLR camera needs to perform the following steps:
- Open the first curtain to start live view.
- Close the second curtain to stop live view, then recock the shutter by returning both curtains to their original positions.
- Release the shutter to take a picture.
- Recock the shutter again.
- Open the first curtain again to resume live view.
This process means that two shutter actuations are required to take a picture in live view. Note that in continuous shooting mode, it may not be necessary to resume live view between shots, reducing the number of extra actuations required.
However, the way the shutter works on the OM-D E-M5 Mark II (and presumably most other mirrorless system cameras, including the E-M1 Mark III) is different. Since there is no optical viewfinder, the camera needs to be able to provide a continuous live view feed, so the shutter needs to be left open during normal operation. As such, the shutter is designed so that it can recock only the first curtain after an exposure, leaving the sensor exposed; the second curtain need not be recocked until the next picture is taken. The steps to take a picture are therefore as follows:
- (immediately after a previous exposure) Open and cock the first curtain only, leaving the sensor exposed for live view.
- Close and cock the second curtain to stop live view.
- Release the shutter to take a picture.
- Open and cock the first curtain again to expose the sensor and resume live view.
This process only requires one shutter actuation for each picture taken, regardless of shooting mode.
To answer the question, I did end up getting the OM-D E-M1 Mark III last week and I can confirm that it counts only one mechanical shutter actuation per shot in any drive mode that uses the mechanical shutter.