If you constantly forward through south, it will be done.
If you go south, you will hit Antarctica sure. This is true for both the flat and globe earth.
If you go in a STRAIGHT direction (not compas angle) in relation to earth, you would easily be able to find paths on a globe earth which never hits Antarctica, while on the current flat earth model, you would always hit the ice wall of Antarctica.
I am not saying it can be easily done however, since we primarily use our compass bearings for navigation, and it would be hard to maintain a straight direction for 20.000 km.
If it was possible to create a craft which always moved straight in relation to the earth (being curved or flat), it would be possible to do this observation and test, But besides firing a long range ballistic missile or a rocket, it would be hard to accomplish.