But, even then it could be argued that Enterprise is more in line with the 2009 universe than the Prime universe.
Logically, no. ENT is common to both universes, by definition, since Nero's incursion occurred decades after it took place.
In the novels it is generally considered that Kirk achieved command of the Enterprise around late-2264/early-2265.
But the Enterprise
was not his FIRST command, was it? I thought he had command of a smaller destroyer-type ship before that. Possibly while at a lower rank, like Commander.