Definitely, the generator could be faulty and still sort of test ok. I once had a corvair with 12v generator that passed all my home tests...it even ran as a motor on the bench. Never could get it to charge the battery. Took it to the starter rebuild shop and they said the armature was bad. They rebuilt it (reverse thread on the armature was an issue that prolonged the process and caused me to have to wait for a replacement armature to be custom made) and all was well in the world. Without a growler, it might be difficult to fully home test the generator.
