Hello, I also started WaniKani as a lower intermediate learner, so I know where you’re coming from.
If you go at a good (but not crazy fast) pace you should be around level 12/13 by the end of August. That means you will know most of N5/N4 Kanji and 1/3 of N3 Kanji, in addition to some N1 and N2 Kanji. If you’re already lower intermediate then you will know all these Kanji really well by that time and it will definitely help you in the placement test.
Before, I felt like I knew most of the Kanji, but after doing the first levels of WK I finally feel those basic 400ish Kanji are really burned in my mind. At around level 14-15 things will start ramping up really fast and you start wishing that things were actually slower
And by this time, it will actually aid you in your university studies.
Also remember that you will be acquiring some vocabulary along the way, so even in the earlier levels I felt like I was learning something, even though I knew 90% of the content.
Since you are on a tight timeline, it may be beneficial to use other methods to reinforce what you’re learning, but if you just cram everything it probably won’t be good for long-term learning. That’s why I would still recommend you sticking to WK so you can continue learning for the long term.
Now that I’m at level 35 after about 9 months, I can start reading more advanced books and materials and I don’t feel overwhelmed when I pick up a random book or I look at a news article. There’s still a ton to learn, but I feel like I covered most of what is needed to be functional without being overwhelmed and that’s probably a quicker learning than you’d get in 8-9 months at any course.
Hope this helps!
EDIT: I am assuming from your post that you’re hoping to be placed at a N3 class. As in, a class that you’re learning the N3 contents… and not to have passed N3… If that’s the case, WK will still be helpful, if you need to know all of N3 contents, then you will be far from that goal.