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").
BlinkLearning partners with major publishers to offer digital textbooks. You can buy a "license" for "Werkstatt A1" that gives you 12–24 months of access to the digital book, plus integrated audio and interactive exercises. werkstatt a1 pdf