I have a SP3 that has previously consistently had an issue using the SD Card to store OneDrive. The SD card would momentarily disconnect then reconnect causing OneDrive to error. For me this would occur constantly every hour or so. Due to this problem I had to keep my OneDrive set to use the internal HD only.
Yesterday I updated my Surface Pro 3 to the Windows 10 Anniversary update version 1607. I decided to try again setting my OneDrive to be stored on the SD card and now one day later I am happy to report I have not experienced any problems at all with OneDrive.
It is very nice to now be able to save space on my hard drive. I’m off to order a larger SD card for my Surface Pro!