Wanikani’s algorithm is essentially this: If you don’t remember the item, it will show it to you more often. If you do remember it, it will show it to you less often.
So, if you remember it because of study outside of Wanikani, then Wanikani’s algorithm will react accordingly and show you the item less often (as it should).
The only way to really ‘break’ the algorithm is if you always study items just before they come up for quiz, for the sake of passing the quiz. Doing so would give the algorithm a false sense of whether you know the items. (But, of course, that still means you are studying the items, which means there’s a chance you are learning them well anyway. So it may or may not matter.)