There is a whole lot more to a word than its definition. How to use it in a sentence, level of politeness, nuances in meaning, countable/uncountable, male/female, etc. This can’t possibly be done consciously for every word out of the thousands of words that need to be learned.
Conversation
True, but that in itself is not an argument against some conscious learning and explicit teaching of grammar and vocab. Research is clear on the value of explicit vocab teaching, for example (eg Nation, Barcroft).
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Any papers that measure acquisition instead of learning? E.g. by not giving the learners the chance to use the monitor, like in spontaneous conversation.
You are using Krashen’s language, not necessarily the language used by other scholars these days. But yes, there is plenty of such research, eg referred to by writers like Leow, Lightbown, Spada, DeKeyser. See Goo et el’s (2015) metastudy (abstract here benjamins.com/catalog/sibil.)
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The nearest to a consensus these days, as I read it, is that most learning is implicit (what K calls acquisition), but that focus on form is very useful and can, directly or indirectly, become ‘acquired’. I’ve just been reading this by Lightbown and Spada s3.amazonaws.com/academia.edu.d