The time is certainly right for their meeting, at least in the original timeline. She also was not a member of Starfleet though. I guess maybe that's changed if this is true.
Well it has never been confirmed if she was ever in Starfleet when she was young. Some people join the service for a few years then get out to pursue their career. In WNMHGB, Mitchell did reference that, “little blonde lab tech I aimed at you.”
And Kirk, shocked, said, “I almost married her!”
That certainly does link Gary Mitchell with Carol Marcus.