I went this route so I’d say it is definitely doable. Wanikani was the perfect tool for me to learn kanji efficiently, though we didn’t progress specifically in JLPT order - we did Genki 1 and 2 over the course of two semesters and 20-ish new kanji per week based on the content in those textbooks.
I’m not familiar with the book, but if you do one Wanikani level per week (pretty much the fastest speed possible), you’ll have done the all the lessons for N5 kanji within 16 weeks. Not that I know when your exams are going to be, but I bet there’s going to be lots of overlap between the kanji you need to study for your exams and the content available to you on Wanikani as you level up.
@CoffeeFuel already posted the specific levels, but here’s the table anyway.
@FarcasA1 If you haven’t read it already, I recommend reading this guide so you’ll know how to best make use of Wanikani as a study tool that suits your goals. It was really helpful for me when I started out.
Best of luck and ganbatte! 
