Question: "One thing I am curious about is the shutter with regards to off camera flash. Is there still a physical shutter that limits me to a max synch speed of around 1/200 of a second? Or have they moved to an electronic shutter that would allow much faster synch times?"

In order to appropriately respond to the question lets first understand how mirrorless camera sensors operate. Most mirorless cameras use CMOS sensors that contain light sensitive pixels arranged in rows. These sensors are always live as long as the camera is powered on and booted up.In the mirrorless world, the sensor information is being constantly fed to the LCD and/or the electronic viewfinder. When you press the shutter the following sequence takes place: a) the sensor is wiped clean electronically; b) next the sensor is turned on and receives light while the pixels record the information; c) now the computer in the camera reads the data collected by the sensor pixels to generate the image. This data is finally recorded to the memory card.We know that the sensor is sensitive to light and always receiving information. In order to capture a good image, the sensor should be restricted from receiving light while it is being wiped clean and then again when it is reading the data captured during exposure. As the sensor data is being read you do not want the pixel information changing with any new light that may fall on the pixels. So, for both these events, mirrorless cameras use electronic or mechanical shutters or a combination of the two.The electronic shutter works by first erasing all the pixel data on a row-by-row basis. Then new image information is gathered and the data is read by the computer on a row-by-row basis very similar to how a television picture is generated. All of this takes time, albeit just a fraction. The greater the number of pixels the more the rows of information and the slower the process. This limits the cameras from achieving high shutter speeds. For proper exposure these rows of pixels gather the same amount of light but do so a row at a time. The data is read at the same rate. The collective time determines the fastest achievable electronic shutter speed.We are aware that to expose properly for flash photography all the pixels must be “alive” and ready to receive data while the flash is on. If the row by row read process starts too early then you will get areas of dark under exposure. In order to properly expose for flash, the computer in the camera has to wait before it can start reading the data collected by the sensor. This wait time determines the highest sync speed for flash photography.As an adjunct to this, in order to achieve higher shutter speeds mirrorless cameras use mechanical second curtains. The curtain can rapidly close all light from entering the sensor while the computer reads the information. On the Sony A7 that has a 24 MP sensor, there are 4000 rows of pixels. The only way to attain shutter speeds of 1/8000 sec. is possible using a mechanical rear-curtain. On the 36 MP A7r however, there are 4912 rows of pixels. To attain speeds of 1/8000 sec. this camera needs both a front-curtain and a rear-curtain shutter. The MFT cameras like the Panasonic GH4 and the Olympus OM-D series have 16 MP sensors that have only 3456 rows and can achieve 1/8000 sec. electronic shutter speeds without the need for mechanical shutters..The Sony A7 has an optional mechanical front-curtain that must be deployed when using lenses of longer focal lengths at high shutter speeds.Unlike DSLR’s, the mechanical shutter on mirrorless cameras remains in an open state in both the powered off and powered on modes, allowing for live view data to be collected and displayed continuously.The highest flash sync speed is currently 1/320 sec on the Olympus OM-D E-M1 , 1/250 sec on the Panasonic GH4 and under 1/200 sec for most of the Sony cameras.Hope this explains why the current mirrorless technology is limited and high flash sync speeds are not feasible.  If you have other photography related questions, please do not hesitate to ask and I will do my best to get you answers.