Quinto is the easy one to get for a TV show. At least he's a TV actor. The rest of the cast has done mostly movies. You'll have a lot harder time getting them to agree to a TV show.
Karl Urban is an excellent television actor, and I feel a regular role on a major TV show would greatly appeal to him. Pine might like the increased recognition as well. I'm not sure about Yelchin or Cho, given that their roles would be minor for such generally bigger stars.
The major problem would be the cost. These major stars' salaries would be astronomical for a TV series, and I don't think anyone would like Battlestar Galactica-level special effects either. Episodes would cost millions upon millions of dollars and even a huge promotional campaign would bring even a fraction of the wanted audience for such a show.
If a TV show happens... it won't be J.J. Abrams Enterprise-based. If it is, it'll be a massive economic failure.
I, personally, believe a subtle, well-written animated series (in any Star Trek era) could be done and ready as a tie-in for the next film, sort of like Star Wars.