I think he'll be hot to rush in without full awareness of what's going on like alt-Kirk demonstrated in "A Quality of Mercy". But he'll learn to listen and understand the situation like Pike. I think Pike will be SNW-Kirk's mentor for the Enterprise captaincy in S2.
This was an interesting interview with Anson Mount on
Esquire
"For you, what’s the essential difference between Pike and Kirk?
There are very few things that I’ve learned in making a long-running TV show. But one trick I’ve learned is that no matter what you do, you’re always putting down footprints that you’re going to have to tread again. So, in the beginning, you try to be careful not to press those footprints too deep. You go in saying to yourself, "Okay, just be careful of how much you think you know."
There are very few things that I know for sure. But one thing that I told [showrunner] Henry [Alonso Myers] is that at the end of all of this, we think the defining quality of Kirk is machismo or bravado. The defining characteristic for Picard, perhaps, is intellect. I would like that defining quality for Pike to be the heart. That’s the best I can put it. Hopefully, Pike can give Kirk just enough of that heart for Kirk to avoid making the kinds of mistakes that he makes in this episode."