It's not essential for the movie actors to participate in a hypothetical animated series. The Clone Wars, for one, proved that.
Indeed. There are plenty of animated adaptations of movie franchises, but it's rare for them to use the actual movie casts; they usually go with similar-sounding substitute actors.
Just to cite a few examples, let's look at the recent shows based on DreamWorks movies. Dragons: Riders of Berk
has Jay Baruchel, America Ferreira, Christopher Mintz-Plasse, and T.J. Miller reprising their characters from How to Train Your Dragon
, but everyone else is recast. Kung Fu Panda: Legends of Awesomeness
has only Lucy Liu and James Hong from the movie cast. And the new Monsters vs. Aliens
cartoon has none of the movie cast involved.
Other examples: The Real Ghostbusters
had no cast members in common with the movie (in fact, Ernie Hudson auditioned to play Winston on the cartoon but was rejected for not sounding Winston-like enough!). Men in Black: The Series
had only Tony Shalhoub and Vincent D'Onofrio returning from the movie, and everyone else was recast, without even any particular attempt to imitate the film actors' voices. Godzilla: The Series
had Kevin Dunn and Malcolm Danare returning from the movie, and that was it. The MTV Spider-Man
CGI cartoon that was meant to be a sequel to the first Raimi movie had none of its cast members reprising their roles (although it did get Michael Clark Duncan to reprise Kingpin from the Daredevil
There have been some cases where cartoon adaptations have featured the original cast, true. Filmation was often pretty good at getting the original cast. TOS had everyone but Walter Koenig. The New Adventures of Gilligan
had everyone but Tina Louise, with Ginger recast. The '77 New Adventures of Batman
had Adam West and Burt Ward, although Lennie Weinrib, Melendy Britt, and Lou Scheimer played everyone else. But they also had their share of shows with actors recast. The Brady Kids
initially had the same child stars as The Brady Bunch
but recast many of them later on. My Favorite Martians
had Jonathan Harris and Howard Morris replacing Ray Walston and Bill Bixby in the leads.
So if there were a Trek cartoon based on the Abramsverse, there's no guarantee it would get many or most of the films' cast. Probably Pine and Saldana are too big to be available or affordable. Cho and Yelchin seem to be rising stars too, so it's hard to say. Pegg might be willing; he has voice-acting experience.