The shield is not supported since is not included in the list, take a look at this document: https://communities.intel.com/docs/DOC-21855. If you have one we encourage you to try it with the Galileo and post your results since they could be useful to other users.
I don’t have this shield but I’ve compiled the examples provided with the library that comes with the shield and I didn’t have any problem, it compiled without errors. Also I reviewed the file WeatherShield1.h and WeatherShield1.cpp and I haven’t found any avr dependency, I think just the string library could give an error since it has an issue with the concatenation but besides that I think the library should work as it is. I hope this works for you.