The shield is not currently supported, you can take a look to the list of supported shields https://communities.intel.com/docs/DOC-21855. If you get one we encourage you to try it and post your results, maybe they’ll help other users. I recommend to check the library of the shield before you get one and try to see if you are able to compile some examples, this is to make sure that there aren't any AVR dependencies or functions that are not implemented yet, if this is the case you could create your own functions to substitute the ones that are not working. Then if you compile the example sketches successfully without errors the shield is very likely to work but that doesn't guarantee that the board will work perfectly.
I have tried to compile one of the e-Health sample sketch and found that there were compilation errors on AVR dependencies.
According to the cooking-hack forum, they are working on making the product compatible with Galileo.