Re: New Info! (Bad Robot press event/villain ID'd, etc.) *SPOILERS*
Carol Marcus being in Starfleet, and on the Enterprise, is another one of those silly small universe syndrome ideas.
In the Prime universe, it's highly unlikely. She and her whole group were shown to be civilian scientists, and her son had a hatred against anything Starfleet (which certainly would have played out differently when "she was one of them once").
Not necesarily. Even if we assume Prime Carol Marcus was once in Starfleet, we don't know the circumstances for why she left. She could have left under less than pleasnt circumstances and her bitterness towards Starfleet could have rubbed off on David causing him to actively hate Starfleet.
"Internet message boards aren't as funny today as they were ten years ago. I've stopped reading new posts." -The Simpsons 20th anniversary special.