Actually, being Admiral Marcus' daughter made her a part of the storyline itself.
Only formally so. She still had basically no impact on the actual events in the movie.
I mean, break it down:
She sneaks aboard pretending to be a "weapons expert." Spock deems her redundant and later figures out her deception.
She is then recruited to take Spock's place in reprising the "surgery on a torpedo" scene with Bones. She then resolves a crisis with the torpedo, but with a random act of desperation that requires no particular expertise. IOW Bones could have been sent out with Sulu, Chekov, Spock or basically almost anyone else and achieved the same result.
She comes back aboard and gets some desultory by-play with Kirk, plus a nice bikini shot. (Or does the bikini happen earlier?)
The
Vengeance confronts the
Enterprise, and this Carol Marcus' moment. She goes head to head with her corrupt father and tells him that he makes her ashamed. Impact? None; he simply has her beamed to his ship and continues his assault. (I sometimes wonder if they didn't originally have a very different plan for this little sequence, which as it is feels totally superfluous.)
She's in the middle of the fighting on the
Vengeance, in which she plays no role apart from having her leg broken by Khan.
And... that's pretty much it, right? That's Carol Marcus in STID. A series of superfluous story beats apart from one scene in which she could be easily replaced by any number of other characters, and the one scene that everyone
really remembers which consists of her stripping off for no particular reason. That's not really what I call being "part of the storyline."