Here’s my short answer because it’s late:
Yes, starting with manga is a great idea. Wonderful supplement. However, starting with Bleach is probably not a good idea, as it will use a lot of strange fantasy vocabulary (which WK will not teach). I believe in Seireitei they even use archaic Japanese (closer to what they spoke in the feudal era?). This seems to be true in the anime, so I’d expect the same of the manga upon which it is based. So there may be this other kind of Japanese being used - as well as other (higher) levels of politeness while in Seireitei.
Something like Yotsubato or Non Non Biyori is going to be a better starting manga.
I’m sure other, more advanced people, will have even better recommendations for you.