You might run into some problems importing your Azure Government publish settings file into SQL Server. However you can still backup to Azure Government Storage Accounts using the Storage Account keys.
Step 1: Create a credential
CREATE CREDENTIAL <name of cred> WITH IDENTITY='<the storage account name>', SECRET='<one of the storage account keys>'
Step 2: create the backup using the credential you created
BACKUP DATABASE <name of db> TO URL = N'<backup endpoint>'
WITH CREDENTIAL = N'<name of cred>'
, NOFORMAT, NOINIT, NAME = N'<name of backup>', NOSKIP, NOREWIND, NOUNLOAD, STATS = 10
The backup endpoint should look like this
https://<storage account name>.blob.core.usgovcloudapi.net/<container name>/<file name>.bak