Hi ChemicalOli,
I've just searched for information about that shield and it seems to be compatible with the Edison Arduino kit at least in the hardware side since the shield uses an I2C interface and the Edison also has I2C interface. Regarding the software side, Adafruit offers the library for the shield however I'm not sure if it will work with Edison. Apparently it is compatible with Galileo, so you could try using it with the Edison in order to know if the library is also compatible with Edison.
#if defined(__AVR__) || defined(__i386__) //compatibility with Intel Galileo
Unfortunately I don't have the shield to test it and make sure it is 100% compatible, but if you decide to try using the shield I invite you to post your results in the Community.
Regards,
Diego.