Yes, it is possible to update BigSky via MIDI sysex.
The current shipping firmware version is 1.44 (released November 2017). The update file, release notes, and instructions can be downloaded at the following link. Update instructions are included as a PDF with the download. 🙂
Firmware Rev. 1.44 (Released November 2017)
For a list of all firmware revision release notes, please click HERE.