I tried something similar about five years ago, and I can relate my experiences to you. I've always had problems learning languages. While I pretty much aced my other classes just by showing up, I really had to hunker down and STUDY to get a decent grade. As a side note, I think that I really learned HOW to study effectively because I needed to for that class.
At any rate, about five years ago, I was planning a trip to Europe. I was seeing some friends in Italy, but my travels were also taking me to Marseille for about a week, and while I have enough Italian to funtion with directions and basic consumer transactions, my command of French was limited to "Oui" and "Merci". Watching French movies, I could barely recognize it as a language, while Italian films I can can sometimes recognize a phrase or word AS an Italian word that I know (kind of a language cocktail party effect), and I can grasp about 80% of a German film if I watch it without subtitles.
I spent about six months listening to French language MP3s while working. Granted, a lot of the repetition made a bunch of words stick in my brain, and, as expected, I was able to order in restaurants, ask directions, and, most importantly, ask if someone could speak English. Interestingly though, when I FIRST arrived in France and was listening to a conversation, I found that I was able to recognize individual words. I didn't know what the words were, but I could distinguish it from the stream of gibberish long enough to ask, "What does ----- mean?"
From having spent time in Italy, I do know that full immersion in a language is the best way to pick it up, and it took me about a week to ten days to start recognizing words. The fact that I could recognize individual French words the day I landed is, I suspect, due to my listening to a bunch of French prior to the trip.
As @NeuronQ mentioned, passive learning can lead to a shallow understanding. But in my case, even that shallow understanding was helpful. Will this technique work with other subjects that you may wish to learn? I don't know. I've been listening to a lot of MIT open courseware lately, and while I'm nowhere near proficient on anything I've listened to, I sometimes find myself recalling a fact, a study, a statistic...much like I recall a story I've heard on the radio.
The fact is that we retain the input our brains receive...which may by the answer to your question, depending upon how you define "learning". Retention, I think is a different matter. Use it or lose it.
My experiences with language lead me to beleive that yes, passive learning is possible. However, that learning only goes so far. More intensive, repetitive study and/or regular use of the skill is necessary to RETAIN what I've learned.