Answer:
Yes, the Beatles know about the Beatles Cartoons- there's even a picture of a mural of the Beatles Cartoons and the Beatles in front of it. The only Beatle that liked it I'm pretty sure was George (I could be wrong about later in each of their careers, because I want to say that John had commented about the cartoon, but, again, I could be wrong. If I am, don't shoot me- I'm just the piano player). The others didn't really like their cartoon character, and I can see why- Cartoon John was the "leader," and didn't seem to take his job seriously; Cartoon Paul was John's "follower;" Cartoon Ringo was always the butt of the jokes mentioned in the cartoon.