I think this thread is talking about two different things, but using the term "grammar" for both of them. When I use the term grammar, I'm talking about identifying parts of speech (noun, verb, etc), parts of a sentence (subject, predicate, direct object, etc), and clauses (dependent, independent) and all the concepts that build on these basic ones.

But I think, when we talk about learning grammar by osmosis, people are actually talking about usage (subject/verb agreement, etc) and mechanics (punctuation, capitalization, etc).

So, yes, I think that one could learn usage and mechanics to a great degree by osmosis, but I don't think that one is going to learn grammar itself by osmosis.