Given that at least 99% of the people who see the movie will never read or even hear of the comic, they would never make the movie in such a way that you'd need to read the comic to understand it. Surely anything in the comic that's relevant to the movie will be explained in the movie as well, in the same way that the events of the first Countdown
were just a fleshed-out version of the same information that Spock Prime's mind meld conveyed in the movie. In that case, the movie was written first, and then the comic took one piece of that film's backstory and expanded on it as a bonus for that tiny fraction of the audience that's into comics. No doubt the same is true here as well.
(It's the same thing we novelists do all the time. You don't need to read The Buried Age
to understand "The Battle" or "The Measure of a Man" -- it just takes background information that's already in those episodes and fleshes it out more fully.)