As best as I can tell, while the -c switch is there to set sovereign clouds, it does not appear the rover login command uses it at all.
As a workaround, I was able to log directly in to Azure Government using the az cli and then I could use rover.
I believe that somewhere near here that another if statement needs to be added, and if -c is set, to execute an az cloud set --name <cloud> prior to executing az login