I'm thinking the answer is 'yes.'
I was given almost no formal instruction in grammar at all as a child, and my years in Spanish class didn't make up for it. Yet when I finally began to learn formal grammar just two years ago, I discovered that nearly all of my writing follows the traditional prescriptive rules of written grammar, up to and including the prohibition against dangling participles.*
I learned all of the rules by reading. (And writing, but mostly, I think, by reading.)
The question is: if it was easy for me to learn applied grammar by reading, and I think it was, why isn't easy for most students today?
Have to catch a train, so more later.
* I didn't quite have the who-whom distinction, but close.