This is something that’s been on my mind as I’ve started reading through Detective Conan in Japanese, having read the material in English a few years ago. Reading has been going a lot more smoothly than I anticipated, and I can’t tell if it’s because I’m at a good level of Japanese for reading it, or if I’m unconsciously filling in knowing the full context (including what happens later)
I’m not familiar with Death Note to comment on what the impact might be, but in general, you should consider manga you’re reading in Japanese to be in one of two categories:
1) Material you already know. This would be something you’ve read in a language you’re fluent in or watched an anime counterpart in a language you know (especially if the manga and anime line up closely with one another).
Here, you have a “superpower” when reading in that you already know what’s being said, and what the context is. It makes it easier to keep going forward. You have to ensure you’re taking the time to pick out any words you don’t know that you want to learn, or any grammar you’re unfamiliar with that you’d like to learn more about. Even then, you’re less likely to make significant gains along the way.
Note: First-time/beginning readers likely will still make significant advances in grammar if they’re not familiar with the basics yet because at that point you can’t so easily plop known context on top of a sentence and feel like you understood it.
2) Material you don’t know. Even if it’s available in some form in a language you know, you haven’t read/seen it before. You have no idea what to expect, and if a line doesn’t make sense, you’re on your own (unless you’re in a book club!) figuring it out.
In this case, you really have to make certain you’re understanding each word and all the grammar. You can’t rely on familiarity. You have to go into full “decipher mode” to work your way through it (unless you already know a lot of the vocabulary and have a lot of experience with grammar). This can be a painful experience for first-time readers, but a necessary one to get into reading. You’ll be learning a lot as you go (again, unless you’re already at a high enough level).
Since I’m reading multiple manga, I like to have at least one where I’m already familiar with the material, and at least one where it’s completely new to me.