If you watched every episode with simultaneous Japanese and English captions, you technically could. Just need to focus on memorizing things and writing things down, as well as deciphering grammar.
Yeah, you would learn some things, but you'd end up speaking like cringy middle schooler. Business and daily life conversations are significantly different from anime and manga ones.
Most american cartoons are made for children and young adults at most. Anime doesn't really have this limitation (more akin to e.g. Bojack Horseman/ Rick and Morty, but could also be a serious drama)
Yeah but also if someone learned English from stuff like the Simpsons, futurama, family guy, etc they’d absolutely still sound weird in their word choices, but also in their understanding of our culture. And yeah bojack and Rick and Morty would do it too. Hell you could even throw some stuff like breaking bad in there and they’d still struggle.