In 1974, E. Hatch ("Second language learning - universals" in: Working Papers on Bilingualism, 3) made a distinction between "data-gatherers" and "rule-formers". Data-gatherers tend to focus more on the development of fluency rather than accuracy, while rule-formers adopt a more analytic, rule-based approach.
A study by Suzanne Graham (Effective Language Learning, 1997) found that problems can arise when a data-gatherer is encouraged to take a more analytical approach to grammar learning (e.g. the German case system). On the other hand, learners who had been categorised as rule-formers later appeared to have developed elements of data-gathering.
One of the most influential theories about explicit learning or instruction (which includes grammar rules) and language acquisition, is Stephen Krashen's theory. Krashen claimed that "learning" (i.e. from formal instruction) and "acquisition" are separate; when you acquire a language in a classroom, this is not the result of formal instruction but of the comprehensible input provided by the teacher. This extreme position is also known as the "non-interface position" (i.e. no interface between formal instruction and language acquisition). (Stephen Krashen uses "acquisition" as a technical term; for example, native speakers acquire their first language in a natural way. So in Stephen Krashen's view, acquisition can occur without "learning".) According to Krashen, learning and "Conscious Learning" can happen only when specific conditions are met (see e.g. his KOTESOL 2011 paper.)
(Note that Krashen's non-interface position, though influential, does not represent anything like a consensus in second language acquisition theory. See for example Rod Ellis' weak interface position.)
Another interesting publication in this context is Grammar and Its Teaching: Challenging the Myths by Diane Larsen-Freeman.