CBS does seem like the by far the most likely channel to air it, at that ('cause rights and such).
Theoretically, except that of all the broadcast networks, CBS has historically been the one least interested in airing science fiction programming. And their upcoming fall schedule has absolutely no SF in it unless you count Person of Interest
, which is borderline at best. So I don't see CBS being eager to air a space show, even one owned by their corporate partners, because it doesn't fit their network identity.
And while production companies and TV networks tend to share common corporate owners and umbrella names these days, they're still separate entities, and networks do air shows produced by other conglomerates' production houses; for instance, Fringe
is produced by Warner Bros. but airs on FOX rather than The CW. So while it's nice and cozy if a show's production company and its network are owned by the same conglomerate, it's not a requirement.
Of the major broadcast networks that still exist, the two that have historically bought and aired the largest number of SF/fantasy shows (or rather, whose genre shows have been the largest percentage of their total lineup) are FOX and NBC. Based on that, I'd consider them the most likely candidates to want to pick up a new Star Trek
series -- perhaps NBC in particular because they have a history with it.