Is the Disney animated series of The Avengers: Earth's Mightiest Heroes canon to the whole series?
No, there are currently no animated shows that are part of the Marvel Cinematic Universe.
Marvel identifies the majority of their thousands of canon universes by giving them an "universe number". These are referred to occasionally in the Official Handbook of the Marvel Universe, and the Jeff Christiansen (the most recent author of those books) keeps an Appendix which includes all of the numbered universes. So, it's usually pretty simple to figure out if two movies or TV shows or comic books take place in the same canon.
The Marvel Cinematic Universe is Earth-199999, and includes all movies produced directly by Marvel Studios (starting with Iron Man), plus the live-action ABC shows (two, so far) and the live-action Netflix shows (three, so far). It will presumably include any future live-action movies or TV shows that fall into those categories, but no animated shows yet.
The animated TV show Avengers: Earth's Mightiest Heroes takes place in Earth-8096, which also included Wolverine and the X-Men plus two animated made-for-TV movies (a Hulk movie and a Thor movie).
After Avengers: Earth's Mightiest Heroes was cancelled, Marvel replaced it with Avengers Assemble. That show takes place in Earth-12041, which is the shared universe for all of Marvel's animated shows currently airing on Disney's network, plus the cancelled Hulk and the Agents of SMASH. While those shows are generally written to have the same "tone" as the MCU movies, and have similar storylines and even some chartacter background, they are different canon universes.
Until now there is no animated show canon to Marvel Cinematic Universe. Even Guardians of the Galaxy (TV series) is also not canon, even when it's a continuation of the Guardians of the Galaxy film.
Anyway, it's also been clear from the team members too, as Ant-Man/Giant-Man, Iron Man, the Hulk, Wasp and Thor are the founding members of The Avengers: Earth's Mightiest Heroes, but in MCU Hank Pym is not part of the Avengers and Scott Lang didn't joined the Avengers team until now. And we have only been shown the Wasp costume in the end credits of the Ant-man film.