Yes, if used correctly. The "Werkstatt" method focuses on application, which is precisely what the Goethe A1 exam tests. However, you need to add separate listening practice (from YouTube or DW) and a mock exam booklet (e.g., "Mit Erfolg zu Start Deutsch 1").
Reviewers highlight its focus on "real-world" German rather than just academic theory. werkstatt a1 pdf