That's a cute sentiment but there is no evidence that merely being exposed to a foreign language necessarily allows you to learn that language. I think you're confusing the movie 13th Warrior for reality.
I have friends who religiously watch subtitled anime only and they are no closer to learning Japanese in any real sense of the word than a person who would watch the dubs, except for picking up a stray random word here or there, but knowing that kawaii means "cute" doesn't give you even a superficial understanding of Japanese. For that, you need to at least pick up hiragana and katakana.
Learning a language requires deliberate work. There is no shortcut.
I speak Spanish. Subtitles have helped me a lot when languages are similar. I watched three seasons of a Catalan TV show subtitled in Spanish, and now I can follow conversations and read it. Before that I wasn't able to understand spoken Catalan.
Subtitles won't really help with sentence structure or conjugations, but it does help a lot with building vocabulary once you have the basics of sentence structure.
I have friends who religiously watch subtitled anime only and they are no closer to learning Japanese in any real sense of the word than a person who would watch the dubs, except for picking up a stray random word here or there, but knowing that kawaii means "cute" doesn't give you even a superficial understanding of Japanese. For that, you need to at least pick up hiragana and katakana.
Learning a language requires deliberate work. There is no shortcut.