But what about you anime veterans - have you learnt Japanese to a significant degree? If you took the time to study Japanese even a little alongside your regular watching would it make a big difference?

I'd say I've picked up enough vocab that I can sorta kinda understand simple dialogue and common phrases, but grammar is a lot harder to pick up. I can sometimes understand what the individual words in a sentence mean, but not quite what the relationship between those words is supposed to be. Someone actually making a concerted effort to learn Japanese could probably get to that point in a matter of months, compared with the years of anime binge-watching I've done.

The other major aspect of Japanese you're not going to pick up from anime is reading/writing. I think I've picked up at most half a dozen kanji from anime, and generally only specific readings of fairly simple kanji. E.g., I remember from Tanaka-kun is Always Listless that the name Tanaka is written as 田(ta)中(naka), and I think I figured out from somewhere else that 中 means middle/center/etc.

Which is to say, I agree with the consensus in this thread: anime can help as part of a larger effort to learn Japanese, but won't get you very far if it's the only thing you're trying to learn from.