Currently the Splunk Add-on for Microsoft Cloud Services does NOT work with Azure Government out of the box, however, it's easy to tweak so that it does. All you need to do is a find and replace on the following:
login.windows.net for login-us.windows.net
management.azure.com for management.usgovcloudapi.net
That aside, from what I understand, the Splunk team is working on enhancing the add-on to support Azure Government and should be rolling out a preview in the coming months.
Disclaimer: I'm from Microsoft's Azure Government Engineering team and would be more than happy to help you, you can reach us at firstname.lastname@example.org