I think that depends on the person and/or language.
My Polish grammar knowledge is now pretty impressive, but I'm having a terrible time trying to remember words, so spend the majority of my time attempting to force memorisation with flash cards.
In a way it's kinda fun - I can go through pages of grammar exercises, conjugating and declining correctly, but with no idea of what Marta did in the past with 101 of somebody's somethings.
However, if you don't have a grasp of the basic grammar you're prone to confuse the person you're talking to. If you're reading, then you lose the context.
Exceptions abound, but I have found this to be true quite often while studying French.
That said, phonology is neglected. Poor pronunciation makes verbal communication more error prone, something you don't need as a beginner, and if you rely entirely on body language for catching such non-lexical content as emphasis and modality, you will suffer when you talk on the phone. A bit of extra work here when you start learning a language will pay off.
In the case of Japanese too, the problem is not the grammar. Japanese morphology is simple (e.g. nouns are the same in singular and plural, verb conjugation doesn't vary with person) and very regular. The big problems are 1) acquiring the vocabulary in the first place, which is hard because the writing system is even less helpful than English's 2) and remembering all those words, which is hard because for the most part they don't resemble either my native language or English.
Grammar learning and engagement might just be the holy grail of learning a language. I haven't come up with a good way of "hacking" grammar. So far it has just been a brute force study of grammar in front of a desk with a lamp.
Tips welcome.
Most of the posts I see on HN mostly revolve around learning languages. In my opinion that's only part of the problem. It's more difficult to get the structure of sentences and tenses correct. I personally know words in 2 - 3 languages which share a root with my mother tongue, but it doesn't mean that I can speak those languages because I often don't get the way a single word transforms based on the tense, part of speech etc. For eg. merely knowing the word "smile" would only take you so far. Knowing the difference between "He is smiling", "He smiles", "He keeps smiling at me" is the tricky part.
Perhaps we are obsessed with learning words because it's the easier problem to solve. Learning sentence structure and grammar takes time and effort.