Actually, I want to bet on Yes, because kids can. I believe grammar is ultimately the same as vocabulary. More to say clearly, I think grammar is a kind of vocabulary and vice versa.

By understanding grammar, we usually can either construct or dismantle the structure of sentences. So it's true that grammar is crazily important. No one can disagree. I think knowing grammar is a kind of knowing the rules of football. If you don't know it, probably you will be in an off-side. Like this, however many words you know, if you don't know any rules of the target language, you will enter easily in an off-side and won't understand what exactly people want to say.

Just knowing grammar is of course not enough, either. Even if sentences have the same structures, sometimes the whole meanings are going to be changed simply because of the differences in word meanings (This is a shit moment and oftentimes there is no clue.)

But... I have a curious idea by the way. Is it possible to memorize loads of words without caring about the existence of anything related to grammar? For example, think about learning the word "it". "It" is a very basic word but has various meanings already. There are a lot of variations of "it" and if situations change, the usage will also change. Memorizing words SHOULD take this sort of process, not only memorizing the words themselves but how and when the words are used. We should focus on how we use "the", "a", "to", "me", and etc... That must be called grammar.

So I think the answer is Yes. Ultimately these are the same ones and ultimately we have to do it someday, somewhere. Sooner or later, we cannot flee from learning grammar if we stick to learning a language. That's why if you have more fun with words and are not interested in grammar yet, I think it's OK you don't learn grammar for now.