Seems as thought it might be OK. It's true that very few who study Latin ever develop true fluency, and I think it's because people get mired in the grammatical details.
I believe that the best way to immerse oneself in Latin would be to listen to the Latin Vulgate, especially the New Testament, since you're familiar with the stories already and so that would make it very effective for you to pick the meanings of unfamiliar words out of the familiar context.