It's been 6 months for me. (Technically a year, but I spent my first 6 months grinding kanji via Heisig, I don't recommend this, lol). I am convinced that learning grammar and exposing yourself to the written language is great practice (and you can learn a lot from it). But I am not convinced you can actually reach fluency using this method.
By just reading, you can attain literacy, but your speaking, listening, and writing skills will be far poorer.
Recently I started formal Japanese classes, and while my prior experience of self study mixed with reading VNs has given me a huge advantage in reading and comprehension, my speaking and listening skills really are poor in comparison.
I'm not denigrating this method. It's great for attaining literacy. And certainly fantastic practice for those already in Japanese classes. But those who are considering using this method (especially for independent study) should know that attaining literacy is different from attaining fluency.