I think that's clearly going to be one of the planned arcs for Kirk in the film (this is clear from the final line of the prologue and also from the general theme of what Pike is supposed to say to Kirk in the fuller trailer) so the question is whether they succeed in that attempt.
It's certainly looking like it's not a question of 'if' this is an aspect of the film.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist