Title. Thank you
I don’t really understand what the question is driving at. The answer is “yes”, insofar as learning a vocabulary word means you’re learning at least one reading of each kanji in the word.
Any given word will use either a kunyomi or onyomi reading for each of the kanji in that word. So if all you study are vocabulary, you might never develop an encyclopedic knowledge of every reading for every character, but IME you will passively pick up the most common and least common readings for the kanji.
What the app won’t teach you is the general difference between onyomi and kunyomi and the heuristics needed to infer which reading a given word will use. That takes experience and book learnin’
There are some very rare readings that Wanikani doesn’t teach.